| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% IEEEtran.cls 2007/03/05 version V1.7a
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% This is the official IEEE LaTeX class for authors of the Institute of 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Electrical and Electronics Engineers (IEEE) Transactions journals and
							 | 
						
						
						
							| 
								
							 | 
							
								%% conferences.
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Support sites:
							 | 
						
						
						
							| 
								
							 | 
							
								%% http://www.michaelshell.org/tex/ieeetran/
							 | 
						
						
						
							| 
								
							 | 
							
								%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
							 | 
						
						
						
							| 
								
							 | 
							
								%% and
							 | 
						
						
						
							| 
								
							 | 
							
								%% http://www.ieee.org/
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Based on the original 1993 IEEEtran.cls, but with many bug fixes
							 | 
						
						
						
							| 
								
							 | 
							
								%% and enhancements (from both JVH and MDS) over the 1996/7 version.
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							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Contributors:
							 | 
						
						
						
							| 
								
							 | 
							
								%% Gerry Murray (1993), Silvano Balemi (1993),
							 | 
						
						
						
							| 
								
							 | 
							
								%% Jon Dixon (1996), Peter N"uchter (1996),
							 | 
						
						
						
							| 
								
							 | 
							
								%% Juergen von Hagen (2000), and Michael Shell (2001-2007)
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi, 
							 | 
						
						
						
							| 
								
							 | 
							
								%%                         Jon Dixon, Peter N"uchter,
							 | 
						
						
						
							| 
								
							 | 
							
								%%                         Juergen von Hagen
							 | 
						
						
						
							| 
								
							 | 
							
								%%                         and
							 | 
						
						
						
							| 
								
							 | 
							
								%% Copyright (c) 2001-2007 by Michael Shell
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Current maintainer (V1.3 to V1.7): Michael Shell
							 | 
						
						
						
							| 
								
							 | 
							
								%%                                    See:
							 | 
						
						
						
							| 
								
							 | 
							
								%%                                    http://www.michaelshell.org/
							 | 
						
						
						
							| 
								
							 | 
							
								%%                                    for current contact information.
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Special thanks to Peter Wilson (CUA) and Donald Arseneau
							 | 
						
						
						
							| 
								
							 | 
							
								%% for allowing the inclusion of the \@ifmtarg command 
							 | 
						
						
						
							| 
								
							 | 
							
								%% from their ifmtarg LaTeX package. 
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%%*************************************************************************
							 | 
						
						
						
							| 
								
							 | 
							
								%% Legal Notice:
							 | 
						
						
						
							| 
								
							 | 
							
								%% This code is offered as-is without any warranty either expressed or
							 | 
						
						
						
							| 
								
							 | 
							
								%% implied; without even the implied warranty of MERCHANTABILITY or
							 | 
						
						
						
							| 
								
							 | 
							
								%% FITNESS FOR A PARTICULAR PURPOSE! 
							 | 
						
						
						
							| 
								
							 | 
							
								%% User assumes all risk.
							 | 
						
						
						
							| 
								
							 | 
							
								%% In no event shall IEEE or any contributor to this code be liable for
							 | 
						
						
						
							| 
								
							 | 
							
								%% any damages or losses, including, but not limited to, incidental,
							 | 
						
						
						
							| 
								
							 | 
							
								%% consequential, or any other damages, resulting from the use or misuse
							 | 
						
						
						
							| 
								
							 | 
							
								%% of any information contained here.
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% All comments are the opinions of their respective authors and are not
							 | 
						
						
						
							| 
								
							 | 
							
								%% necessarily endorsed by the IEEE.
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% This work is distributed under the LaTeX Project Public License (LPPL)
							 | 
						
						
						
							| 
								
							 | 
							
								%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
							 | 
						
						
						
							| 
								
							 | 
							
								%% distributed and modified. A copy of the LPPL, version 1.3, is included
							 | 
						
						
						
							| 
								
							 | 
							
								%% in the base LaTeX documentation of all distributions of LaTeX released
							 | 
						
						
						
							| 
								
							 | 
							
								%% 2003/12/01 or later.
							 | 
						
						
						
							| 
								
							 | 
							
								%% Retain all contribution notices and credits.
							 | 
						
						
						
							| 
								
							 | 
							
								%% ** Modified files should be clearly indicated as such, including  **
							 | 
						
						
						
							| 
								
							 | 
							
								%% ** renaming them and changing author support contact information. **
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
							 | 
						
						
						
							| 
								
							 | 
							
								%%                    bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Major changes to the user interface should be indicated by an 
							 | 
						
						
						
							| 
								
							 | 
							
								%% increase in the version numbers. If a version is a beta, it will 
							 | 
						
						
						
							| 
								
							 | 
							
								%% be indicated with a BETA suffix, i.e., 1.4 BETA.
							 | 
						
						
						
							| 
								
							 | 
							
								%% Small changes can be indicated by appending letters to the version
							 | 
						
						
						
							| 
								
							 | 
							
								%% such as "IEEEtran_v14a.cls".
							 | 
						
						
						
							| 
								
							 | 
							
								%% In all cases, \Providesclass, any \typeout messages to the user,
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							 | 
							
								%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the
							 | 
						
						
						
							| 
								
							 | 
							
								%% correct version information.
							 | 
						
						
						
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								%% The changes should also be documented via source comments.
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								%%*************************************************************************
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								%%
							 | 
						
						
						
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							 | 
							
								%
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							 | 
							
								% Available class options 
							 | 
						
						
						
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							 | 
							
								% e.g., \documentclass[10pt,conference]{IEEEtran} 
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								%             *** choose only one from each category ***
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								%
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							 | 
							
								% 9pt, 10pt, 11pt, 12pt
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							 | 
							
								%    Sets normal font size. The default is 10pt.
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
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							 | 
							
								% conference, journal, technote, peerreview, peerreviewca
							 | 
						
						
						
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							 | 
							
								%    determines format mode - conference papers, journal papers,
							 | 
						
						
						
							| 
								
							 | 
							
								%    correspondence papers (technotes), or peer review papers. The user
							 | 
						
						
						
							| 
								
							 | 
							
								%    should also select 9pt when using technote. peerreview is like
							 | 
						
						
						
							| 
								
							 | 
							
								%    journal mode, but provides for a single-column "cover" title page for
							 | 
						
						
						
							| 
								
							 | 
							
								%    anonymous peer review. The paper title (without the author names) is
							 | 
						
						
						
							| 
								
							 | 
							
								%    repeated at the top of the page after the cover page. For peer review
							 | 
						
						
						
							| 
								
							 | 
							
								%    papers, the \IEEEpeerreviewmaketitle command must be executed (will
							 | 
						
						
						
							| 
								
							 | 
							
								%    automatically be ignored for non-peerreview modes) at the place the
							 | 
						
						
						
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							 | 
							
								%    cover page is to end, usually just after the abstract (keywords are
							 | 
						
						
						
							| 
								
							 | 
							
								%    not normally used with peer review papers). peerreviewca is like
							 | 
						
						
						
							| 
								
							 | 
							
								%    peerreview, but allows the author names to be entered and formatted
							 | 
						
						
						
							| 
								
							 | 
							
								%    as with conference mode so that author affiliation and contact
							 | 
						
						
						
							| 
								
							 | 
							
								%    information can be easily seen on the cover page.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is journal.
							 | 
						
						
						
							| 
								
							 | 
							
								%
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							 | 
							
								% draft, draftcls, draftclsnofoot, final
							 | 
						
						
						
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							 | 
							
								%    determines if paper is formatted as a widely spaced draft (for
							 | 
						
						
						
							| 
								
							 | 
							
								%    handwritten editor comments) or as a properly typeset final version.
							 | 
						
						
						
							| 
								
							 | 
							
								%    draftcls restricts draft mode to the class file while all other LaTeX
							 | 
						
						
						
							| 
								
							 | 
							
								%    packages (i.e., \usepackage{graphicx}) will behave as final - allows
							 | 
						
						
						
							| 
								
							 | 
							
								%    for a draft paper with visible figures, etc. draftclsnofoot is like
							 | 
						
						
						
							| 
								
							 | 
							
								%    draftcls, but does not display the date and the word "DRAFT" at the foot
							 | 
						
						
						
							| 
								
							 | 
							
								%    of the pages. If using one of the draft modes, the user will probably
							 | 
						
						
						
							| 
								
							 | 
							
								%    also want to select onecolumn.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is final.
							 | 
						
						
						
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							 | 
							
								%
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							 | 
							
								% letterpaper, a4paper
							 | 
						
						
						
							| 
								
							 | 
							
								%    determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER
							 | 
						
						
						
							| 
								
							 | 
							
								%    SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS
							 | 
						
						
						
							| 
								
							 | 
							
								%    WILL BE AFFECTED. In particular, documents using the a4paper option will
							 | 
						
						
						
							| 
								
							 | 
							
								%    have reduced side margins (A4 is narrower than US letter) and a longer
							 | 
						
						
						
							| 
								
							 | 
							
								%    bottom margin (A4 is longer than US letter). For both cases, the top
							 | 
						
						
						
							| 
								
							 | 
							
								%    margins will be the same and the text will be horizontally centered. 
							 | 
						
						
						
							| 
								
							 | 
							
								%    For final submission to IEEE, authors should use US letter (8.5 X 11in)
							 | 
						
						
						
							| 
								
							 | 
							
								%    paper. Note that authors should ensure that all post-processing 
							 | 
						
						
						
							| 
								
							 | 
							
								%    (ps, pdf, etc.) uses the same paper specificiation as the .tex document.
							 | 
						
						
						
							| 
								
							 | 
							
								%    Problems here are by far the number one reason for incorrect margins.
							 | 
						
						
						
							| 
								
							 | 
							
								%    IEEEtran will automatically set the default paper size under pdflatex 
							 | 
						
						
						
							| 
								
							 | 
							
								%    (without requiring a change to pdftex.cfg), so this issue is more
							 | 
						
						
						
							| 
								
							 | 
							
								%    important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for
							 | 
						
						
						
							| 
								
							 | 
							
								%    dvips, or use the dvips -t papersize option instead as needed. See the
							 | 
						
						
						
							| 
								
							 | 
							
								%    testflow documentation
							 | 
						
						
						
							| 
								
							 | 
							
								%    http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/testflow
							 | 
						
						
						
							| 
								
							 | 
							
								%    for more details on dvips paper size configuration.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is letterpaper.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% oneside, twoside
							 | 
						
						
						
							| 
								
							 | 
							
								%    determines if layout follows single sided or two sided (duplex)
							 | 
						
						
						
							| 
								
							 | 
							
								%    printing. The only notable change is with the headings at the top of
							 | 
						
						
						
							| 
								
							 | 
							
								%    the pages.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is oneside.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% onecolumn, twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								%    determines if text is organized into one or two columns per page. One
							 | 
						
						
						
							| 
								
							 | 
							
								%    column mode is usually used only with draft papers.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is twocolumn.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								%    Use the format of the IEEE Computer Society.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% romanappendices
							 | 
						
						
						
							| 
								
							 | 
							
								%    Use the "Appendix I" convention when numbering appendices. IEEEtran.cls
							 | 
						
						
						
							| 
								
							 | 
							
								%    now defaults to Alpha "Appendix A" convention - the opposite of what
							 | 
						
						
						
							| 
								
							 | 
							
								%    v1.6b and earlier did.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
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							 | 
							
								% captionsoff
							 | 
						
						
						
							| 
								
							 | 
							
								%    disables the display of the figure/table captions. Some IEEE journals
							 | 
						
						
						
							| 
								
							 | 
							
								%    request that captions be removed and figures/tables be put on pages
							 | 
						
						
						
							| 
								
							 | 
							
								%    of their own at the end of an initial paper submission. The endfloat
							 | 
						
						
						
							| 
								
							 | 
							
								%    package can be used with this class option to achieve this format.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
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							 | 
							
								% nofonttune
							 | 
						
						
						
							| 
								
							 | 
							
								%    turns off tuning of the font interword spacing. Maybe useful to those
							 | 
						
						
						
							| 
								
							 | 
							
								%    not using the standard Times fonts or for those who have already "tuned"
							 | 
						
						
						
							| 
								
							 | 
							
								%    their fonts.
							 | 
						
						
						
							| 
								
							 | 
							
								%    The default is to enable IEEEtran to tune font parameters.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								%----------
							 | 
						
						
						
							| 
								
							 | 
							
								% Available CLASSINPUTs provided (all are macros unless otherwise noted):
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINPUTbaselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINPUTinnersidemargin
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINPUToutersidemargin
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINPUTtoptextmargin
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINPUTbottomtextmargin
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% Available CLASSINFOs provided:
							 | 
						
						
						
							| 
								
							 | 
							
								% \ifCLASSINFOpdf                       (TeX if conditional)
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINFOpaperwidth                  (macro)
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINFOpaperheight                 (macro)
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINFOnormalsizebaselineskip      (length)
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSINFOnormalsizeunitybaselineskip (length)
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% Available CLASSOPTIONs provided:
							 | 
						
						
						
							| 
								
							 | 
							
								% all class option flags (TeX if conditionals) unless otherwise noted,
							 | 
						
						
						
							| 
								
							 | 
							
								% e.g., \ifCLASSOPTIONcaptionsoff
							 | 
						
						
						
							| 
								
							 | 
							
								% point size options provided as a single macro:
							 | 
						
						
						
							| 
								
							 | 
							
								% \CLASSOPTIONpt
							 | 
						
						
						
							| 
								
							 | 
							
								% which will be defined as 9, 10, 11, or 12 depending on the document's
							 | 
						
						
						
							| 
								
							 | 
							
								% normalsize point size.
							 | 
						
						
						
							| 
								
							 | 
							
								% also, class option peerreviewca implies the use of class option peerreview
							 | 
						
						
						
							| 
								
							 | 
							
								% and classoption draft implies the use of class option draftcls
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ProvidesClass{IEEEtran}[2007/03/05 V1.7a by Michael Shell]
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- http://www.michaelshell.org/tex/ieeetran/}
							 | 
						
						
						
							| 
								
							 | 
							
								\NeedsTeXFormat{LaTeX2e}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran.cls version numbers, provided as of V1.3
							 | 
						
						
						
							| 
								
							 | 
							
								% These values serve as a way a .tex file can
							 | 
						
						
						
							| 
								
							 | 
							
								% determine if the new features are provided.
							 | 
						
						
						
							| 
								
							 | 
							
								% The version number of this IEEEtrans.cls can be obtained from 
							 | 
						
						
						
							| 
								
							 | 
							
								% these values. i.e., V1.4
							 | 
						
						
						
							| 
								
							 | 
							
								% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-
							 | 
						
						
						
							| 
								
							 | 
							
								% (no need to enumerate "a" minor changes here)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEtransversionmajor{1}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEtransversionminor{7}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% These do nothing, but provide them like in article.cls
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@restonecol
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@titlepage
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% class option conditionals
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONonecolumn       \CLASSOPTIONonecolumnfalse
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONtwocolumn       \CLASSOPTIONtwocolumntrue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONoneside         \CLASSOPTIONonesidetrue
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONtwoside         \CLASSOPTIONtwosidefalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONfinal           \CLASSOPTIONfinaltrue
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONdraft           \CLASSOPTIONdraftfalse
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONdraftcls        \CLASSOPTIONdraftclsfalse
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONdraftclsnofoot  \CLASSOPTIONdraftclsnofootfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONpeerreview      \CLASSOPTIONpeerreviewfalse
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONpeerreviewca    \CLASSOPTIONpeerreviewcafalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONjournal         \CLASSOPTIONjournaltrue
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONconference      \CLASSOPTIONconferencefalse
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONtechnote        \CLASSOPTIONtechnotefalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONnofonttune      \CLASSOPTIONnofonttunefalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONcaptionsoff     \CLASSOPTIONcaptionsofffalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONcompsoc         \CLASSOPTIONcompsocfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSOPTIONromanappendices \CLASSOPTIONromanappendicesfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% class info conditionals
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% indicates if pdf (via pdflatex) output
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifCLASSINFOpdf               \CLASSINFOpdffalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6b internal flag to show if using a4paper
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEusingAfourpaper       \@IEEEusingAfourpaperfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran class scratch pad registers
							 | 
						
						
						
							| 
								
							 | 
							
								% dimen
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\@IEEEtrantmpdimenA
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\@IEEEtrantmpdimenB
							 | 
						
						
						
							| 
								
							 | 
							
								% count
							 | 
						
						
						
							| 
								
							 | 
							
								\newcount\@IEEEtrantmpcountA
							 | 
						
						
						
							| 
								
							 | 
							
								\newcount\@IEEEtrantmpcountB
							 | 
						
						
						
							| 
								
							 | 
							
								% token list
							 | 
						
						
						
							| 
								
							 | 
							
								\newtoks\@IEEEtrantmptoksA
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we use \CLASSOPTIONpt so that we can ID the point size (even for 9pt docs)
							 | 
						
						
						
							| 
								
							 | 
							
								% as well as LaTeX's \@ptsize to retain some compatability with some
							 | 
						
						
						
							| 
								
							 | 
							
								% external packages
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@ptsize{0}
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{9pt}{\def\CLASSOPTIONpt{9}\def\@ptsize{0}}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{10pt}{\def\CLASSOPTIONpt{10}\def\@ptsize{0}}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{11pt}{\def\CLASSOPTIONpt{11}\def\@ptsize{1}}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{12pt}{\def\CLASSOPTIONpt{12}\def\@ptsize{2}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%
							 | 
						
						
						
							| 
								
							 | 
							
								                            \setlength{\paperwidth}{8.5in}%
							 | 
						
						
						
							| 
								
							 | 
							
								                            \@IEEEusingAfourpaperfalse
							 | 
						
						
						
							| 
								
							 | 
							
								                            \def\CLASSOPTIONpaper{letter}%
							 | 
						
						
						
							| 
								
							 | 
							
								                            \def\CLASSINFOpaperwidth{8.5in}%
							 | 
						
						
						
							| 
								
							 | 
							
								                            \def\CLASSINFOpaperheight{11in}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%
							 | 
						
						
						
							| 
								
							 | 
							
								                        \setlength{\paperwidth}{210mm}%
							 | 
						
						
						
							| 
								
							 | 
							
								                        \@IEEEusingAfourpapertrue
							 | 
						
						
						
							| 
								
							 | 
							
								                        \def\CLASSOPTIONpaper{a4}%
							 | 
						
						
						
							| 
								
							 | 
							
								                        \def\CLASSINFOpaperwidth{210mm}%
							 | 
						
						
						
							| 
								
							 | 
							
								                        \def\CLASSINFOpaperheight{297mm}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{oneside}{\@twosidefalse\@mparswitchfalse
							 | 
						
						
						
							| 
								
							 | 
							
								                        \CLASSOPTIONonesidetrue\CLASSOPTIONtwosidefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{twoside}{\@twosidetrue\@mparswitchtrue
							 | 
						
						
						
							| 
								
							 | 
							
								                        \CLASSOPTIONtwosidetrue\CLASSOPTIONonesidefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{onecolumn}{\CLASSOPTIONonecolumntrue\CLASSOPTIONtwocolumnfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{twocolumn}{\CLASSOPTIONtwocolumntrue\CLASSOPTIONonecolumnfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% If the user selects draft, then this class AND any packages
							 | 
						
						
						
							| 
								
							 | 
							
								% will go into draft mode.
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{draft}{\CLASSOPTIONdrafttrue\CLASSOPTIONdraftclstrue
							 | 
						
						
						
							| 
								
							 | 
							
								                      \CLASSOPTIONdraftclsnofootfalse} 
							 | 
						
						
						
							| 
								
							 | 
							
								% draftcls is for a draft mode which will not affect any packages
							 | 
						
						
						
							| 
								
							 | 
							
								% used by the document.
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{draftcls}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
							 | 
						
						
						
							| 
								
							 | 
							
								                         \CLASSOPTIONdraftclsnofootfalse} 
							 | 
						
						
						
							| 
								
							 | 
							
								% draftclsnofoot is like draftcls, but without the footer.
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{draftclsnofoot}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue
							 | 
						
						
						
							| 
								
							 | 
							
								                               \CLASSOPTIONdraftclsnofoottrue} 
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{final}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclsfalse
							 | 
						
						
						
							| 
								
							 | 
							
								                      \CLASSOPTIONdraftclsnofootfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{journal}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
							 | 
						
						
						
							| 
								
							 | 
							
								                        \CLASSOPTIONjournaltrue\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{conference}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
							 | 
						
						
						
							| 
								
							 | 
							
								                           \CLASSOPTIONjournalfalse\CLASSOPTIONconferencetrue\CLASSOPTIONtechnotefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{technote}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse
							 | 
						
						
						
							| 
								
							 | 
							
								                         \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotetrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{peerreview}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcafalse
							 | 
						
						
						
							| 
								
							 | 
							
								                           \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{peerreviewca}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcatrue
							 | 
						
						
						
							| 
								
							 | 
							
								                             \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{nofonttune}{\CLASSOPTIONnofonttunetrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{captionsoff}{\CLASSOPTIONcaptionsofftrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{compsoc}{\CLASSOPTIONcompsoctrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOption{romanappendices}{\CLASSOPTIONromanappendicestrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% default to US letter paper, 10pt, twocolumn, one sided, final, journal
							 | 
						
						
						
							| 
								
							 | 
							
								\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}
							 | 
						
						
						
							| 
								
							 | 
							
								% overrride these defaults per user requests
							 | 
						
						
						
							| 
								
							 | 
							
								\ProcessOptions
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Computer Society conditional execution command
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\relax#1\relax\fi\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								% inverse
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEnotcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\else\relax#1\relax\fi\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEcompsocconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\relax#1\relax\fi\fi\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc not conference
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEcompsocnotconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\else\relax#1\relax\fi\fi\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses Times Roman font, so we'll default to Times.
							 | 
						
						
						
							| 
								
							 | 
							
								% These three commands make up the entire times.sty package.
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\sfdefault}{phv}
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\rmdefault}{ptm}
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\ttdefault}{pcr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsoconly{\typeout{-- Using IEEE Computer Society mode.}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font,
							 | 
						
						
						
							| 
								
							 | 
							
								% not Times Roman.
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% enable Times/Palatino main text font
							 | 
						
						
						
							| 
								
							 | 
							
								\normalfont\selectfont
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 conference notice message hook
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEconsolenoticeconference{\typeout{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{** Conference Paper **}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{Before submitting the final camera ready copy, remember to:}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ 1. Manually equalize the lengths of two columns on the last page}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ of your paper;}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ uses only Type 1 fonts and that every step in the generation}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ process uses the appropriate paper size.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we can send console reminder messages to the user here
							 | 
						
						
						
							| 
								
							 | 
							
								\AtEndDocument{\ifCLASSOPTIONconference\@IEEEconsolenoticeconference\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% warn about the use of single column other than for draft mode
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtwocolumn\else%
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifCLASSOPTIONdraftcls\else%
							 | 
						
						
						
							| 
								
							 | 
							
								   \typeout{** ATTENTION: Single column mode is not typically used with IEEE publications.}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 improved paper size setting code.
							 | 
						
						
						
							| 
								
							 | 
							
								% Set pdfpage and dvips paper sizes. Conditional tests are similar to that
							 | 
						
						
						
							| 
								
							 | 
							
								% of ifpdf.sty. Retain within {} to ensure tested macros are never altered,
							 | 
						
						
						
							| 
								
							 | 
							
								% even if only effect is to set them to \relax.
							 | 
						
						
						
							| 
								
							 | 
							
								% if \pdfoutput is undefined or equal to relax, output a dvips special
							 | 
						
						
						
							| 
								
							 | 
							
								{\@ifundefined{pdfoutput}{\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}}{%
							 | 
						
						
						
							| 
								
							 | 
							
								% pdfoutput is defined and not equal to \relax
							 | 
						
						
						
							| 
								
							 | 
							
								% check for pdfpageheight existence just in case someone sets pdfoutput
							 | 
						
						
						
							| 
								
							 | 
							
								% under non-pdflatex. If exists, set them regardless of value of \pdfoutput.
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifundefined{pdfpageheight}{\relax}{\global\pdfpagewidth\paperwidth
							 | 
						
						
						
							| 
								
							 | 
							
								\global\pdfpageheight\paperheight}%
							 | 
						
						
						
							| 
								
							 | 
							
								% if using \pdfoutput=0 under pdflatex, send dvips papersize special
							 | 
						
						
						
							| 
								
							 | 
							
								\ifcase\pdfoutput
							 | 
						
						
						
							| 
								
							 | 
							
								\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								% we are using pdf output, set CLASSINFOpdf flag
							 | 
						
						
						
							| 
								
							 | 
							
								\global\CLASSINFOpdftrue
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% let the user know the selected papersize
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- Using \CLASSINFOpaperwidth\space x \CLASSINFOpaperheight\space
							 | 
						
						
						
							| 
								
							 | 
							
								(\CLASSOPTIONpaper)\space paper.}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSINFOpdf
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- Using PDF output.}
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- Using DVI output.}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% The idea hinted here is for LaTeX to generate markleft{} and markright{}
							 | 
						
						
						
							| 
								
							 | 
							
								% automatically for you after you enter \author{}, \journal{},
							 | 
						
						
						
							| 
								
							 | 
							
								% \journaldate{}, journalvol{}, \journalnum{}, etc.
							 | 
						
						
						
							| 
								
							 | 
							
								% However, there may be some backward compatibility issues here as
							 | 
						
						
						
							| 
								
							 | 
							
								% well as some special applications for IEEEtran.cls and special issues
							 | 
						
						
						
							| 
								
							 | 
							
								% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.
							 | 
						
						
						
							| 
								
							 | 
							
								% We'll leave this as an open future suggestion.
							 | 
						
						
						
							| 
								
							 | 
							
								%\newcommand{\journal}[1]{\def\@journal{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								%\def\@journal{}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% pointsize values
							 | 
						
						
						
							| 
								
							 | 
							
								% used with ifx to determine the document's normal size
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEptsizenine{9}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEptsizeten{10}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEptsizeeleven{11}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEptsizetwelve{12}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% FONT DEFINITIONS (No sizexx.clo file needed) 
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 revised font sizes, displayskip values and
							 | 
						
						
						
							| 
								
							 | 
							
								%      revised normalsize baselineskip to reduce underfull vbox problems
							 | 
						
						
						
							| 
								
							 | 
							
								%      on the 58pc = 696pt = 9.5in text height we want
							 | 
						
						
						
							| 
								
							 | 
							
								%      normalsize     #lines/column  baselineskip (aka leading)
							 | 
						
						
						
							| 
								
							 | 
							
								%             9pt     63             11.0476pt (truncated down)
							 | 
						
						
						
							| 
								
							 | 
							
								%            10pt     58             12pt      (exact)
							 | 
						
						
						
							| 
								
							 | 
							
								%            11pt     52             13.3846pt (truncated down)
							 | 
						
						
						
							| 
								
							 | 
							
								%            12pt     50             13.92pt   (exact)
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we need to store the nominal baselineskip for the given font size
							 | 
						
						
						
							| 
								
							 | 
							
								% in case baselinestretch ever changes.
							 | 
						
						
						
							| 
								
							 | 
							
								% this is a dimen, so it will not hold stretch or shrink
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\@IEEEnormalsizeunitybaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEnormalsizeunitybaselineskip\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizenine
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- This is a 9 point document.}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEnormalsizeunitybaselineskip}{11.0476pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayskip 1.5ex plus3pt minus1pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayskip \abovedisplayskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayshortskip 0pt plus3pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayshortskip 1.5ex plus3pt minus1pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\small{\@setfontsize{\small}{8.5}{10pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								% sublargesize is the same as large - 10pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\large{\@setfontsize{\large}{10}{12pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Large{\@setfontsize{\Large}{12}{14pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\huge{\@setfontsize{\huge}{17}{20pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Huge{\@setfontsize{\Huge}{20}{24pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Check if we have selected 10 points
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizeten
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- This is a 10 point document.}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayskip 1.5ex plus4pt minus2pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayskip \abovedisplayskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayshortskip 0pt plus4pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayshortskip 1.5ex plus4pt minus2pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\small{\@setfontsize{\small}{9}{10pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tiny{\@setfontsize{\tiny}{5}{6pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								% sublargesize is a tad smaller than large - 11pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\large{\@setfontsize{\large}{12}{14pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Large{\@setfontsize{\Large}{14}{17pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\huge{\@setfontsize{\huge}{20}{24pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Check if we have selected 11 points
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizeeleven
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- This is an 11 point document.}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEnormalsizeunitybaselineskip}{13.3846pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayskip 1.5ex plus5pt minus3pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayskip \abovedisplayskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayshortskip 0pt plus5pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayshortskip 1.5ex plus5pt minus3pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\small{\@setfontsize{\small}{10}{12pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								% sublargesize is the same as large - 12pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\large{\@setfontsize{\large}{12}{14pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Large{\@setfontsize{\Large}{14}{17pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\huge{\@setfontsize{\huge}{20}{24pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Check if we have selected 12 points
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizetwelve
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{-- This is a 12 point document.}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEnormalsizeunitybaselineskip}{13.92pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayskip 1.5ex plus6pt minus4pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayskip \abovedisplayskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\abovedisplayshortskip 0pt plus6pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\belowdisplayshortskip 1.5ex plus6pt minus4pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\small{\@setfontsize{\small}{10}{12pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tiny{\@setfontsize{\tiny}{6}{7pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								% sublargesize is the same as large - 14pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\large{\@setfontsize{\large}{14}{17pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Large{\@setfontsize{\Large}{17}{20pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\huge{\@setfontsize{\huge}{22}{26pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\Huge{\@setfontsize{\Huge}{24}{28pt}}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 The Computer Modern Fonts will issue a substitution warning for
							 | 
						
						
						
							| 
								
							 | 
							
								% 24pt titles (24.88pt is used instead) increase the substitution
							 | 
						
						
						
							| 
								
							 | 
							
								% tolerance to turn off this warning
							 | 
						
						
						
							| 
								
							 | 
							
								\def\fontsubfuzz{.9pt}
							 | 
						
						
						
							| 
								
							 | 
							
								% However, the default (and correct) Times font will scale exactly as needed.
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% warn the user in case they forget to use the 9pt option with
							 | 
						
						
						
							| 
								
							 | 
							
								% technote
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote%
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizenine\else%
							 | 
						
						
						
							| 
								
							 | 
							
								  \typeout{** ATTENTION: Technotes are normally 9pt documents.}%
							 | 
						
						
						
							| 
								
							 | 
							
								 \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7
							 | 
						
						
						
							| 
								
							 | 
							
								% Improved \textunderscore to provide a much better fake _ when used with
							 | 
						
						
						
							| 
								
							 | 
							
								% OT1 encoding. Under OT1, detect use of pcr or cmtt \ttfamily and use
							 | 
						
						
						
							| 
								
							 | 
							
								% available true _ glyph for those two typewriter fonts.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstringptm{ptm} % Times Roman family
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstringppl{ppl} % Palatino Roman family
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstringphv{phv} % Helvetica Sans Serif family
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstringpcr{pcr} % Courier typewriter family
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstringcmtt{cmtt} % Computer Modern typewriter family
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareTextCommandDefault{\textunderscore}{\leavevmode
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\f@family\@IEEEstringpcr\string_\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\f@family\@IEEEstringcmtt\string_\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\f@family\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\f@family\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\f@family\@IEEEstringphv\kern -0.03em\vbox{\hrule\@width 0.62em\@height 0.52pt\kern -0.33ex}\kern -0.03em\else
							 | 
						
						
						
							| 
								
							 | 
							
								\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}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% set the default \baselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								\def\baselinestretch{1}
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\baselinestretch{1.5}% default baselinestretch for draft modes
							 | 
						
						
						
							| 
								
							 | 
							
								\fi 
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process CLASSINPUT baselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSINPUTbaselinestretch\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								  \edef\baselinestretch{\CLASSINPUTbaselinestretch} % user CLASSINPUT override
							 | 
						
						
						
							| 
								
							 | 
							
								  \typeout{** ATTENTION: Overriding \string\baselinestretch\space to
							 | 
						
						
						
							| 
								
							 | 
							
								           \baselinestretch\space via \string\CLASSINPUT.}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize % make \baselinestretch take affect
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% store the normalsize baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\CLASSINFOnormalsizebaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\CLASSINFOnormalsizebaselineskip=\baselineskip\relax
							 | 
						
						
						
							| 
								
							 | 
							
								% and the normalsize unity (baselinestretch=1) baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% we could save a register by giving the user access to
							 | 
						
						
						
							| 
								
							 | 
							
								% \@IEEEnormalsizeunitybaselineskip. However, let's protect
							 | 
						
						
						
							| 
								
							 | 
							
								% its read only internal status
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\CLASSINFOnormalsizeunitybaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\CLASSINFOnormalsizeunitybaselineskip=\@IEEEnormalsizeunitybaselineskip\relax
							 | 
						
						
						
							| 
								
							 | 
							
								% store the nominal value of jot
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEnormaljot
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEnormaljot=0.25\baselineskip\relax
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% set \jot
							 | 
						
						
						
							| 
								
							 | 
							
								\jot=\IEEEnormaljot\relax
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6, we are now going to fine tune the interword spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% The default interword glue for Times under TeX appears to use a
							 | 
						
						
						
							| 
								
							 | 
							
								% nominal interword spacing of 25% (relative to the font size, i.e., 1em)
							 | 
						
						
						
							| 
								
							 | 
							
								% a maximum of 40% and a minimum of 19%.
							 | 
						
						
						
							| 
								
							 | 
							
								% For example, 10pt text uses an interword glue of:
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% 2.5pt plus 1.49998pt minus 0.59998pt
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% However, IEEE allows for a more generous range which reduces the need
							 | 
						
						
						
							| 
								
							 | 
							
								% for hyphenation, especially for two column text. Furthermore, IEEE
							 | 
						
						
						
							| 
								
							 | 
							
								% tends to use a little bit more nominal space between the words.
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE's interword spacing percentages appear to be:
							 | 
						
						
						
							| 
								
							 | 
							
								% 35% nominal
							 | 
						
						
						
							| 
								
							 | 
							
								% 23% minimum
							 | 
						
						
						
							| 
								
							 | 
							
								% 50% maximum
							 | 
						
						
						
							| 
								
							 | 
							
								% (They may even be using a tad more for the largest fonts such as 24pt.)
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% for bold text, IEEE increases the spacing a little more:
							 | 
						
						
						
							| 
								
							 | 
							
								% 37.5% nominal
							 | 
						
						
						
							| 
								
							 | 
							
								% 23% minimum
							 | 
						
						
						
							| 
								
							 | 
							
								% 55% maximum
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% here are the interword spacing ratios we'll use
							 | 
						
						
						
							| 
								
							 | 
							
								% for medium (normal weight)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceratioM{0.35}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceMINratioM{0.23}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceMAXratioM{0.50}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% for bold
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceratioB{0.375}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceMINratioB{0.23}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEinterspaceMAXratioB{0.55}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% command to revise the interword spacing for the current font under TeX:
							 | 
						
						
						
							| 
								
							 | 
							
								% \fontdimen2 = nominal interword space
							 | 
						
						
						
							| 
								
							 | 
							
								% \fontdimen3 = interword stretch
							 | 
						
						
						
							| 
								
							 | 
							
								% \fontdimen4 = interword shrink
							 | 
						
						
						
							| 
								
							 | 
							
								% since all changes to the \fontdimen are global, we can enclose these commands
							 | 
						
						
						
							| 
								
							 | 
							
								% in braces to confine any font attribute or length changes
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@@IEEEsetfontdimens#1#2#3{{%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontdimen2\font=\@IEEEtrantmpdimenA\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontdimen3\font=-\@IEEEtrantmpdimenA\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% revise the interword spacing for each font weight
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEsetfontdimens{{%
							 | 
						
						
						
							| 
								
							 | 
							
								\mdseries
							 | 
						
						
						
							| 
								
							 | 
							
								\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%
							 | 
						
						
						
							| 
								
							 | 
							
								\bfseries
							 | 
						
						
						
							| 
								
							 | 
							
								\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%
							 | 
						
						
						
							| 
								
							 | 
							
								}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% revise the interword spacing for each font shape
							 | 
						
						
						
							| 
								
							 | 
							
								% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are
							 | 
						
						
						
							| 
								
							 | 
							
								% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we
							 | 
						
						
						
							| 
								
							 | 
							
								% won't alter these either.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsetfontdimens{{%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalfont
							 | 
						
						
						
							| 
								
							 | 
							
								\@@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\normalfont\itshape
							 | 
						
						
						
							| 
								
							 | 
							
								\@@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% command to revise the interword spacing for each font size (and shape
							 | 
						
						
						
							| 
								
							 | 
							
								% and weight). Only the \rmfamily is done here as \ttfamily uses a 
							 | 
						
						
						
							| 
								
							 | 
							
								% fixed spacing and \sffamily is not used as the main text of IEEE papers.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtunefonts{{\selectfont\rmfamily
							 | 
						
						
						
							| 
								
							 | 
							
								\tiny\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\scriptsize\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\footnotesize\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\small\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\sublargesize\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\large\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\LARGE\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\huge\@IEEEsetfontdimens
							 | 
						
						
						
							| 
								
							 | 
							
								\Huge\@IEEEsetfontdimens}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% if the nofonttune class option is not given, revise the interword spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% now - in case IEEEtran makes any default length measurements, and make
							 | 
						
						
						
							| 
								
							 | 
							
								% sure all the default fonts are loaded
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONnofonttune\else
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtunefonts
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% and again at the start of the document in case the user loaded different fonts
							 | 
						
						
						
							| 
								
							 | 
							
								\AtBeginDocument{\ifCLASSOPTIONnofonttune\else\@IEEEtunefonts\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX is a little to quick to use hyphenations
							 | 
						
						
						
							| 
								
							 | 
							
								% So, we increase the penalty for their use and raise
							 | 
						
						
						
							| 
								
							 | 
							
								% the badness level that triggers an underfull hbox
							 | 
						
						
						
							| 
								
							 | 
							
								% warning. The author may still have to tweak things,
							 | 
						
						
						
							| 
								
							 | 
							
								% but the appearance will be much better "right out
							 | 
						
						
						
							| 
								
							 | 
							
								% of the box" than that under V1.5 and prior.
							 | 
						
						
						
							| 
								
							 | 
							
								% TeX default is 50
							 | 
						
						
						
							| 
								
							 | 
							
								\hyphenpenalty=750
							 | 
						
						
						
							| 
								
							 | 
							
								% If we didn't adjust the interword spacing, 2200 might be better.
							 | 
						
						
						
							| 
								
							 | 
							
								% The TeX default is 1000
							 | 
						
						
						
							| 
								
							 | 
							
								\hbadness=1350
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE does not use extra spacing after punctuation
							 | 
						
						
						
							| 
								
							 | 
							
								\frenchspacing
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 increase this a tad to discourage equation breaks
							 | 
						
						
						
							| 
								
							 | 
							
								\binoppenalty=1000 % default 700
							 | 
						
						
						
							| 
								
							 | 
							
								\relpenalty=800     % default 500
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% margin note stuff
							 | 
						
						
						
							| 
								
							 | 
							
								\marginparsep      10pt
							 | 
						
						
						
							| 
								
							 | 
							
								\marginparwidth    20pt
							 | 
						
						
						
							| 
								
							 | 
							
								\marginparpush     25pt
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% if things get too close, go ahead and let them touch
							 | 
						
						
						
							| 
								
							 | 
							
								\lineskip            0pt
							 | 
						
						
						
							| 
								
							 | 
							
								\normallineskip      0pt
							 | 
						
						
						
							| 
								
							 | 
							
								\lineskiplimit       0pt
							 | 
						
						
						
							| 
								
							 | 
							
								\normallineskiplimit 0pt
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% The distance from the lower edge of the text body to the
							 | 
						
						
						
							| 
								
							 | 
							
								% footline
							 | 
						
						
						
							| 
								
							 | 
							
								\footskip 0.4in
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% normally zero, should be relative to font height.
							 | 
						
						
						
							| 
								
							 | 
							
								% put in a little rubber to help stop some bad breaks (underfull vboxes)
							 | 
						
						
						
							| 
								
							 | 
							
								\parskip 0ex plus 0.2ex minus 0.1ex
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\parindent    1.0em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\topmargin    -49.0pt
							 | 
						
						
						
							| 
								
							 | 
							
								\headheight   12pt
							 | 
						
						
						
							| 
								
							 | 
							
								\headsep      0.25in
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% use the normal font baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% so that \topskip is unaffected by changes in \baselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								\topskip=\@IEEEnormalsizeunitybaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\textheight       58pc  % 9.63in, 696pt
							 | 
						
						
						
							| 
								
							 | 
							
								% Tweak textheight to a perfect integer number of lines/page.
							 | 
						
						
						
							| 
								
							 | 
							
								% The normal baselineskip for each document point size is used 
							 | 
						
						
						
							| 
								
							 | 
							
								% to determine these values.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=63\@IEEEnormalsizeunitybaselineskip\fi      % 63 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=58\@IEEEnormalsizeunitybaselineskip\fi       % 58 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=52\@IEEEnormalsizeunitybaselineskip\fi    % 52 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=50\@IEEEnormalsizeunitybaselineskip\fi    % 50 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\columnsep         1pc
							 | 
						
						
						
							| 
								
							 | 
							
								\textwidth        43pc   % 2 x 21pc + 1pc = 43pc
							 | 
						
						
						
							| 
								
							 | 
							
								 
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% the default side margins are equal
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEusingAfourpaper 
							 | 
						
						
						
							| 
								
							 | 
							
								\oddsidemargin        14.32mm
							 | 
						
						
						
							| 
								
							 | 
							
								\evensidemargin       14.32mm
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\oddsidemargin        0.680in
							 | 
						
						
						
							| 
								
							 | 
							
								\evensidemargin       0.680in
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% compensate for LaTeX's 1in offset
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\oddsidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\evensidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% adjust margins for conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								 \topmargin        -0.25in
							 | 
						
						
						
							| 
								
							 | 
							
								 % we retain the reserved, but unused space for headers
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\topmargin}{-\headheight}
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\topmargin}{-\headsep}
							 | 
						
						
						
							| 
								
							 | 
							
								 \textheight        9.25in % The standard for conferences (668.4975pt)
							 | 
						
						
						
							| 
								
							 | 
							
								 % Tweak textheight to a perfect integer number of lines/page.
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=61\@IEEEnormalsizeunitybaselineskip\fi      % 61 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=56\@IEEEnormalsizeunitybaselineskip\fi       % 56 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=50\@IEEEnormalsizeunitybaselineskip\fi    % 50 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=48\@IEEEnormalsizeunitybaselineskip\fi    % 48 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								 % compsoc conference use a larger value for columnsep
							 | 
						
						
						
							| 
								
							 | 
							
								 \columnsep 0.375in
							 | 
						
						
						
							| 
								
							 | 
							
								 % compsoc conferences want 1in top margin, 1.125in bottom margin
							 | 
						
						
						
							| 
								
							 | 
							
								 \topmargin        0in
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\topmargin}{-6pt}% we tweak this a tad to better comply with top of line stuff
							 | 
						
						
						
							| 
								
							 | 
							
								 % we retain the reserved, but unused space for headers
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\topmargin}{-\headheight}
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\topmargin}{-\headsep}
							 | 
						
						
						
							| 
								
							 | 
							
								 \textheight        8.875in % (641.39625pt)
							 | 
						
						
						
							| 
								
							 | 
							
								 % Tweak textheight to a perfect integer number of lines/page.
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=58\@IEEEnormalsizeunitybaselineskip\fi      % 58 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=53\@IEEEnormalsizeunitybaselineskip\fi       % 53 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=48\@IEEEnormalsizeunitybaselineskip\fi    % 48 lines/page
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=46\@IEEEnormalsizeunitybaselineskip\fi    % 46 lines/page 
							 | 
						
						
						
							| 
								
							 | 
							
								 \textwidth 6.5in
							 | 
						
						
						
							| 
								
							 | 
							
								 % the default side margins are equal
							 | 
						
						
						
							| 
								
							 | 
							
								 \if@IEEEusingAfourpaper 
							 | 
						
						
						
							| 
								
							 | 
							
								  \oddsidemargin        22.45mm
							 | 
						
						
						
							| 
								
							 | 
							
								  \evensidemargin       22.45mm
							 | 
						
						
						
							| 
								
							 | 
							
								 \else
							 | 
						
						
						
							| 
								
							 | 
							
								  \oddsidemargin        1in
							 | 
						
						
						
							| 
								
							 | 
							
								  \evensidemargin       1in
							 | 
						
						
						
							| 
								
							 | 
							
								 \fi
							 | 
						
						
						
							| 
								
							 | 
							
								 % compensate for LaTeX's 1in offset
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\oddsidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								 \addtolength{\evensidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% draft mode settings override that of all other modes
							 | 
						
						
						
							| 
								
							 | 
							
								% provides a nice 1in margin all around the paper and extra
							 | 
						
						
						
							| 
								
							 | 
							
								% space between the lines for editor's comments
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONdraftcls 
							 | 
						
						
						
							| 
								
							 | 
							
								  % want 1in from top of paper to text
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\topmargin}{-\headsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\topmargin}{-\headheight}%
							 | 
						
						
						
							| 
								
							 | 
							
								  % we want 1in side margins regardless of paper type
							 | 
						
						
						
							| 
								
							 | 
							
								  \oddsidemargin      0in
							 | 
						
						
						
							| 
								
							 | 
							
								  \evensidemargin     0in
							 | 
						
						
						
							| 
								
							 | 
							
								  % set the text width
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\textwidth}{\paperwidth}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textwidth}{-2.0in}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\textheight}{\paperheight}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textheight}{-2.0in}%
							 | 
						
						
						
							| 
								
							 | 
							
								  % digitize textheight to be an integer number of lines.
							 | 
						
						
						
							| 
								
							 | 
							
								  % this may cause the bottom margin to be off a tad
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textheight}{-1\topskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \divide\textheight  by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								  \multiply\textheight  by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textheight}{\topskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process CLASSINPUT inner/outer margin
							 | 
						
						
						
							| 
								
							 | 
							
								% if inner margin defined, but outer margin not, set outer to inner.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSINPUTinnersidemargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifx\CLASSINPUToutersidemargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								    \edef\CLASSINPUToutersidemargin{\CLASSINPUTinnersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSINPUToutersidemargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								  % if outer margin defined, but inner margin not, set inner to outer.
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifx\CLASSINPUTinnersidemargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								    \edef\CLASSINPUTinnersidemargin{\CLASSINPUToutersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\oddsidemargin}{\CLASSINPUTinnersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifCLASSOPTIONtwoside
							 | 
						
						
						
							| 
								
							 | 
							
								    \setlength{\evensidemargin}{\CLASSINPUToutersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \else
							 | 
						
						
						
							| 
								
							 | 
							
								    \setlength{\evensidemargin}{\CLASSINPUTinnersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\oddsidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\evensidemargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\textwidth}{\paperwidth}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textwidth}{-\CLASSINPUTinnersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textwidth}{-\CLASSINPUToutersidemargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \typeout{** ATTENTION: Overriding inner side margin to \CLASSINPUTinnersidemargin\space and 
							 | 
						
						
						
							| 
								
							 | 
							
								           outer side margin to \CLASSINPUToutersidemargin\space via \string\CLASSINPUT.}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process CLASSINPUT top/bottom text margin
							 | 
						
						
						
							| 
								
							 | 
							
								% if toptext margin defined, but bottomtext margin not, set bottomtext to toptext margin
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSINPUTtoptextmargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								    \edef\CLASSINPUTbottomtextmargin{\CLASSINPUTtoptextmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSINPUTbottomtextmargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								  % if bottomtext margin defined, but toptext margin not, set toptext to bottomtext margin
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifx\CLASSINPUTtoptextmargin\@IEEEundefined
							 | 
						
						
						
							| 
								
							 | 
							
								    \edef\CLASSINPUTtoptextmargin{\CLASSINPUTbottomtextmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\topmargin}{\CLASSINPUTtoptextmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\topmargin}{-1in}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\topmargin}{-\headheight}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\topmargin}{-\headsep}
							 | 
						
						
						
							| 
								
							 | 
							
								  \setlength{\textheight}{\paperheight}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textheight}{-\CLASSINPUTtoptextmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\textheight}{-\CLASSINPUTbottomtextmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								  % in the default format we use the normal baselineskip as topskip
							 | 
						
						
						
							| 
								
							 | 
							
								  % we only need 0.7 of this to clear typical top text and we need
							 | 
						
						
						
							| 
								
							 | 
							
								  % an extra 0.3 spacing at the bottom for descenders. This will
							 | 
						
						
						
							| 
								
							 | 
							
								  % correct for both.
							 | 
						
						
						
							| 
								
							 | 
							
								  \addtolength{\topmargin}{-0.3\@IEEEnormalsizeunitybaselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								  \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and 
							 | 
						
						
						
							| 
								
							 | 
							
								           bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% LIST SPACING CONTROLS
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Controls the amount of EXTRA spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% above and below \trivlist 
							 | 
						
						
						
							| 
								
							 | 
							
								% Both \list and IED lists override this.
							 | 
						
						
						
							| 
								
							 | 
							
								% However, \trivlist will use this as will most
							 | 
						
						
						
							| 
								
							 | 
							
								% things built from \trivlist like the \center
							 | 
						
						
						
							| 
								
							 | 
							
								% environment.
							 | 
						
						
						
							| 
								
							 | 
							
								\topsep           0.5\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Controls the additional spacing around lists preceded
							 | 
						
						
						
							| 
								
							 | 
							
								% or followed by blank lines. IEEE does not increase
							 | 
						
						
						
							| 
								
							 | 
							
								% spacing before or after paragraphs so it is set to zero.
							 | 
						
						
						
							| 
								
							 | 
							
								% \z@ is the same as zero, but faster.
							 | 
						
						
						
							| 
								
							 | 
							
								\partopsep          \z@
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Controls the spacing between paragraphs in lists. 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE does not increase spacing before or after paragraphs
							 | 
						
						
						
							| 
								
							 | 
							
								% so this is also zero. 
							 | 
						
						
						
							| 
								
							 | 
							
								% With IEEEtran.cls, global changes to
							 | 
						
						
						
							| 
								
							 | 
							
								% this value DO affect lists (but not IED lists).
							 | 
						
						
						
							| 
								
							 | 
							
								\parsep             \z@
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Controls the extra spacing between list items. 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE does not put extra spacing between items.
							 | 
						
						
						
							| 
								
							 | 
							
								% With IEEEtran.cls, global changes to this value DO affect
							 | 
						
						
						
							| 
								
							 | 
							
								% lists (but not IED lists).
							 | 
						
						
						
							| 
								
							 | 
							
								\itemsep            \z@
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \itemindent is the amount to indent the FIRST line of a list
							 | 
						
						
						
							| 
								
							 | 
							
								% item. It is auto set to zero within the \list environment. To alter
							 | 
						
						
						
							| 
								
							 | 
							
								% it, you have to do so when you call the \list.
							 | 
						
						
						
							| 
								
							 | 
							
								% However, IEEE uses this for the theorem environment
							 | 
						
						
						
							| 
								
							 | 
							
								% There is an alternative value for this near \leftmargini below
							 | 
						
						
						
							| 
								
							 | 
							
								\itemindent         -1em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \leftmargin, the spacing from the left margin of the main text to
							 | 
						
						
						
							| 
								
							 | 
							
								% the left of the main body of a list item is set by \list.
							 | 
						
						
						
							| 
								
							 | 
							
								% Hence this statement does nothing for lists.
							 | 
						
						
						
							| 
								
							 | 
							
								% But, quote and verse do use it for indention.
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmargin         2em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we retain this stuff from the older IEEEtran.cls so that \list
							 | 
						
						
						
							| 
								
							 | 
							
								% will work the same way as before. However, itemize, enumerate and
							 | 
						
						
						
							| 
								
							 | 
							
								% description (IED) could care less about what these are as they
							 | 
						
						
						
							| 
								
							 | 
							
								% all are overridden.
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmargini        2em
							 | 
						
						
						
							| 
								
							 | 
							
								%\itemindent         2em  % Alternative values: sometimes used.
							 | 
						
						
						
							| 
								
							 | 
							
								%\leftmargini        0em
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmarginii       1em
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmarginiii    1.5em
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmarginiv     1.5em
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmarginv      1.0em
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmarginvi     1.0em
							 | 
						
						
						
							| 
								
							 | 
							
								\labelsep         0.5em 
							 | 
						
						
						
							| 
								
							 | 
							
								\labelwidth         \z@
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% The old IEEEtran.cls behavior of \list is retained.
							 | 
						
						
						
							| 
								
							 | 
							
								% However, the new V1.3 IED list environments override all the
							 | 
						
						
						
							| 
								
							 | 
							
								% @list stuff (\@listX is called within \list for the
							 | 
						
						
						
							| 
								
							 | 
							
								% appropriate level just before the user's list_decl is called). 
							 | 
						
						
						
							| 
								
							 | 
							
								% \topsep is now 2pt as IEEE puts a little extra space around
							 | 
						
						
						
							| 
								
							 | 
							
								% lists - used by those non-IED macros that depend on \list.
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that \parsep and \itemsep are not redefined as in 
							 | 
						
						
						
							| 
								
							 | 
							
								% the sizexx.clo \@listX (which article.cls uses) so global changes
							 | 
						
						
						
							| 
								
							 | 
							
								% of these values DO affect \list
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@listI\@listi
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\labelwidth-\labelsep \topsep 2pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\labelwidth-\labelsep \topsep 2pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\labelwidth-\labelsep \topsep 2pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\labelwidth-\labelsep \topsep 2pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\labelwidth-\labelsep \topsep 2pt}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses 5) not 5.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelenumi{\theenumi)}     \def\theenumi{\arabic{enumi}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses a) not (a)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelenumii{\theenumii)}  \def\theenumii{\alph{enumii}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses iii) not iii.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses A) not A.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelenumiv{\theenumiv)}   \def\theenumiv{\Alph{enumiv}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% exactly the same as in article.cls
							 | 
						
						
						
							| 
								
							 | 
							
								\def\p@enumii{\theenumi}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\p@enumiii{\theenumi(\theenumii)}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\p@enumiv{\p@enumiii\theenumiii}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% itemized list label styles
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelitemi{$\scriptstyle\bullet$}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelitemii{\textbf{--}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelitemiii{$\ast$}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\labelitemiv{$\cdot$}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% **** V1.3 ENHANCEMENTS ****
							 | 
						
						
						
							| 
								
							 | 
							
								% Itemize, Enumerate and Description (IED) List Controls
							 | 
						
						
						
							| 
								
							 | 
							
								% ***************************
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE seems to use at least two different values by
							 | 
						
						
						
							| 
								
							 | 
							
								% which ITEMIZED list labels are indented to the right
							 | 
						
						
						
							| 
								
							 | 
							
								% For The Journal of Lightwave Technology (JLT) and The Journal
							 | 
						
						
						
							| 
								
							 | 
							
								% on Selected Areas in Communications (JSAC), they tend to use
							 | 
						
						
						
							| 
								
							 | 
							
								% an indention equal to \parindent. For Transactions on Communications
							 | 
						
						
						
							| 
								
							 | 
							
								% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.
							 | 
						
						
						
							| 
								
							 | 
							
								% We'll provide both values here for you so that you can choose 
							 | 
						
						
						
							| 
								
							 | 
							
								% which one you like in your document using a command such as:
							 | 
						
						
						
							| 
								
							 | 
							
								% setlength{\IEEEilabelindent}{\IEEEilabelindentB}
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEilabelindentA
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEilabelindentA \parindent
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEilabelindentB
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEilabelindentB 1.3\parindent
							 | 
						
						
						
							| 
								
							 | 
							
								% However, we'll default to using \parindent
							 | 
						
						
						
							| 
								
							 | 
							
								% which makes more sense to me
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEilabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEilabelindent \IEEEilabelindentA
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This controls the default amount the enumerated list labels
							 | 
						
						
						
							| 
								
							 | 
							
								% are indented to the right.
							 | 
						
						
						
							| 
								
							 | 
							
								% Normally, this is the same as the paragraph indention
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEelabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEelabelindent \parindent
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This controls the default amount the description list labels
							 | 
						
						
						
							| 
								
							 | 
							
								% are indented to the right.
							 | 
						
						
						
							| 
								
							 | 
							
								% Normally, this is the same as the paragraph indention
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEdlabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEdlabelindent \parindent
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This is the value actually used within the IED lists.
							 | 
						
						
						
							| 
								
							 | 
							
								% The IED environments automatically set its value to
							 | 
						
						
						
							| 
								
							 | 
							
								% one of the three values above, so global changes do 
							 | 
						
						
						
							| 
								
							 | 
							
								% not have any effect
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEElabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEElabelindent \parindent
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% The actual amount labels will be indented is
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEElabelindent multiplied by the factor below
							 | 
						
						
						
							| 
								
							 | 
							
								% corresponding to the level of nesting depth
							 | 
						
						
						
							| 
								
							 | 
							
								% This provides a means by which the user can
							 | 
						
						
						
							| 
								
							 | 
							
								% alter the effective \IEEElabelindent for deeper
							 | 
						
						
						
							| 
								
							 | 
							
								% levels
							 | 
						
						
						
							| 
								
							 | 
							
								% There may not be such a thing as correct "standard IEEE"
							 | 
						
						
						
							| 
								
							 | 
							
								% values. What IEEE actually does may depend on the specific
							 | 
						
						
						
							| 
								
							 | 
							
								% circumstances.
							 | 
						
						
						
							| 
								
							 | 
							
								% The first list level almost always has full indention.
							 | 
						
						
						
							| 
								
							 | 
							
								% The second levels I've seen have only 75% of the normal indentation
							 | 
						
						
						
							| 
								
							 | 
							
								% Three level or greater nestings are very rare. I am guessing
							 | 
						
						
						
							| 
								
							 | 
							
								% that they don't use any indentation.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactori{1.0}   % almost always one
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactoriv{0.0}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactorv{0.0}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactorvi{0.0}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% value actually used within IED lists, it is auto
							 | 
						
						
						
							| 
								
							 | 
							
								% set to one of the 6 values above
							 | 
						
						
						
							| 
								
							 | 
							
								% global changes here have no effect
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEElabelindentfactor{1.0}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This controls the default spacing between the end of the IED
							 | 
						
						
						
							| 
								
							 | 
							
								% list labels and the list text, when normal text is used for
							 | 
						
						
						
							| 
								
							 | 
							
								% the labels.
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEiednormlabelsep
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEiednormlabelsep 0.6em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This controls the default spacing between the end of the IED
							 | 
						
						
						
							| 
								
							 | 
							
								% list labels and the list text, when math symbols are used for
							 | 
						
						
						
							| 
								
							 | 
							
								% the labels (nomenclature lists). IEEE usually increases the 
							 | 
						
						
						
							| 
								
							 | 
							
								% spacing in these cases
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\IEEEiedmathlabelsep
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEiedmathlabelsep 1.2em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This controls the extra vertical separation put above and
							 | 
						
						
						
							| 
								
							 | 
							
								% below each IED list. IEEE usually puts a little extra spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% around each list. However, this spacing is barely noticeable.
							 | 
						
						
						
							| 
								
							 | 
							
								\newskip\IEEEiedtopsep
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEiedtopsep 2pt plus 1pt minus 1pt
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This command is executed within each IED list environment
							 | 
						
						
						
							| 
								
							 | 
							
								% at the beginning of the list. You can use this to set the 
							 | 
						
						
						
							| 
								
							 | 
							
								% parameters for some/all your IED list(s) without disturbing 
							 | 
						
						
						
							| 
								
							 | 
							
								% global parameters that affect things other than lists.
							 | 
						
						
						
							| 
								
							 | 
							
								% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}}
							 | 
						
						
						
							| 
								
							 | 
							
								% will alter the \labelsep for the next list(s) until 
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEiedlistdecl is redefined. 
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEiedlistdecl{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This command provides an easy way to set \leftmargin based
							 | 
						
						
						
							| 
								
							 | 
							
								% on the \labelwidth, \labelsep and the argument \IEEElabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								% Usage: \IEEEcalcleftmargin{width-to-indent-the-label}
							 | 
						
						
						
							| 
								
							 | 
							
								% output is in the \leftmargin variable, i.e., effectively:
							 | 
						
						
						
							| 
								
							 | 
							
								% \leftmargin = argument + \labelwidth + \labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here, shield end of lines with %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\leftmargin}{\labelwidth}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\leftmargin}{\labelsep}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This command provides an easy way to set \labelwidth to the
							 | 
						
						
						
							| 
								
							 | 
							
								% width of the given text. It is the same as
							 | 
						
						
						
							| 
								
							 | 
							
								% \settowidth{\labelwidth}{label-text}
							 | 
						
						
						
							| 
								
							 | 
							
								% and useful as a shorter alternative.
							 | 
						
						
						
							| 
								
							 | 
							
								% Typically used to set \labelwidth to be the width
							 | 
						
						
						
							| 
								
							 | 
							
								% of the longest label in the list
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% When this command is executed, IED lists will use the 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEiedmathlabelsep label separation rather than the normal
							 | 
						
						
						
							| 
								
							 | 
							
								% spacing. To have an effect, this command must be executed via
							 | 
						
						
						
							| 
								
							 | 
							
								% the \IEEEiedlistdecl or within the option of the IED list
							 | 
						
						
						
							| 
								
							 | 
							
								% environments.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% A flag which controls whether the IED lists automatically
							 | 
						
						
						
							| 
								
							 | 
							
								% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								% Useful if you want to specify your own \leftmargin
							 | 
						
						
						
							| 
								
							 | 
							
								% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) 
							 | 
						
						
						
							| 
								
							 | 
							
								% via the \IEEEiedlistdecl or within the option of the IED list
							 | 
						
						
						
							| 
								
							 | 
							
								% environments to have an effect.
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifIEEEnocalcleftmargin
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEnocalcleftmarginfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% A flag which controls whether \IEEElabelindent is multiplied by
							 | 
						
						
						
							| 
								
							 | 
							
								% the \IEEElabelindentfactor for each list level.
							 | 
						
						
						
							| 
								
							 | 
							
								% This flag must be set via the \IEEEiedlistdecl or within the option 
							 | 
						
						
						
							| 
								
							 | 
							
								% of the IED list environments to have an effect.
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifIEEEnolabelindentfactor
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEnolabelindentfactorfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% internal variable to indicate type of IED label
							 | 
						
						
						
							| 
								
							 | 
							
								% justification
							 | 
						
						
						
							| 
								
							 | 
							
								% 0 - left; 1 - center; 2 - right
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEiedjustify{0}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% commands to allow the user to control IED
							 | 
						
						
						
							| 
								
							 | 
							
								% label justifications. Use these commands within
							 | 
						
						
						
							| 
								
							 | 
							
								% the IED environment option or in the \IEEEiedlistdecl
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that changing the normal list justifications
							 | 
						
						
						
							| 
								
							 | 
							
								% is nonstandard and IEEE may not like it if you do so!
							 | 
						
						
						
							| 
								
							 | 
							
								% I include these commands as they may be helpful to
							 | 
						
						
						
							| 
								
							 | 
							
								% those who are using these enhanced list controls for
							 | 
						
						
						
							| 
								
							 | 
							
								% other non-IEEE related LaTeX work.
							 | 
						
						
						
							| 
								
							 | 
							
								% itemize and enumerate automatically default to right
							 | 
						
						
						
							| 
								
							 | 
							
								% justification, description defaults to left.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% commands to save to and restore from the list parameter copies
							 | 
						
						
						
							| 
								
							 | 
							
								% this allows us to set all the list parameters within
							 | 
						
						
						
							| 
								
							 | 
							
								% the list_decl and prevent \list (and its \@list) 
							 | 
						
						
						
							| 
								
							 | 
							
								% from overriding any of our parameters
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 use \edefs instead of dimen's to conserve dimen registers
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here, shield end of lines with %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedlabelwidth{\the\labelwidth}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedlabelsep{\the\labelsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedleftmargin{\the\leftmargin}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedpartopsep{\the\partopsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedparsep{\the\parsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEieditemsep{\the\itemsep}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedrightmargin{\the\rightmargin}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEiedlistparindent{\the\listparindent}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEieditemindent{\the\itemindent}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\labelwidth\@IEEEiedlabelwidth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\labelsep\@IEEEiedlabelsep\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\leftmargin\@IEEEiedleftmargin\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\partopsep\@IEEEiedpartopsep\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\parsep\@IEEEiedparsep\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\itemsep\@IEEEieditemsep\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\rightmargin\@IEEEiedrightmargin\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\listparindent\@IEEEiedlistparindent\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\itemindent\@IEEEieditemindent\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.6b provide original LaTeX IED list environments
							 | 
						
						
						
							| 
								
							 | 
							
								% note that latex.ltx defines \itemize and \enumerate, but not \description
							 | 
						
						
						
							| 
								
							 | 
							
								% which must be created by the base classes
							 | 
						
						
						
							| 
								
							 | 
							
								% save original LaTeX itemize and enumerate
							 | 
						
						
						
							| 
								
							 | 
							
								\let\LaTeXitemize\itemize
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endLaTeXitemize\enditemize
							 | 
						
						
						
							| 
								
							 | 
							
								\let\LaTeXenumerate\enumerate
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endLaTeXenumerate\endenumerate
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide original LaTeX description environment from article.cls
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{LaTeXdescription}
							 | 
						
						
						
							| 
								
							 | 
							
								               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
							 | 
						
						
						
							| 
								
							 | 
							
								                        \let\makelabel\descriptionlabel}}
							 | 
						
						
						
							| 
								
							 | 
							
								               {\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								\newcommand*\descriptionlabel[1]{\hspace\labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								                                 \normalfont\bfseries #1}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% override LaTeX's default IED lists
							 | 
						
						
						
							| 
								
							 | 
							
								\def\itemize{\@IEEEitemize}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\enditemize{\@endIEEEitemize}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\enumerate{\@IEEEenumerate}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endenumerate{\@endIEEEenumerate}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\description{\@IEEEdescription}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\enddescription{\@endIEEEdescription}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide the user with aliases - may help those using packages that
							 | 
						
						
						
							| 
								
							 | 
							
								% override itemize, enumerate, or description
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEitemize{\@IEEEitemize}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEitemize{\@endIEEEitemize}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEenumerate{\@IEEEenumerate}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEenumerate{\@endIEEEenumerate}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEdescription{\@IEEEdescription}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEdescription{\@endIEEEdescription}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 we want to keep the IEEEtran IED list definitions as our own internal
							 | 
						
						
						
							| 
								
							 | 
							
								% commands so they are protected against redefinition
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@endIEEEitemize{\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@endIEEEenumerate{\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@endIEEEdescription{\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
							 | 
						
						
						
							| 
								
							 | 
							
								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran itemized list MDS 1/2001
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here, shield end of lines with %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEitemize[#1]{%
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifnum\@itemdepth>3\relax\@toodeep\else%
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifnum\@listdepth>5\relax\@toodeep\else%
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@itemdepth\@ne%
							 | 
						
						
						
							| 
								
							 | 
							
								                \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
							 | 
						
						
						
							| 
								
							 | 
							
								                % get the labelindentfactor for this level
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth\@ne% we need to know what the level WILL be
							 | 
						
						
						
							| 
								
							 | 
							
								                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth-\@ne% undo our increment
							 | 
						
						
						
							| 
								
							 | 
							
								                \def\@IEEEiedjustify{2}% right justified labels are default
							 | 
						
						
						
							| 
								
							 | 
							
								                % set other defaults
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnocalcleftmarginfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnolabelindentfactorfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \topsep\IEEEiedtopsep%
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEElabelindent\IEEEilabelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                \labelsep\IEEEiednormlabelsep%
							 | 
						
						
						
							| 
								
							 | 
							
								                \partopsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \parsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \rightmargin 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \listparindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                % calculate the label width
							 | 
						
						
						
							| 
								
							 | 
							
								                % the user can override this later if
							 | 
						
						
						
							| 
								
							 | 
							
								                % they specified a \labelwidth
							 | 
						
						
						
							| 
								
							 | 
							
								                \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \@IEEEsavelistparams% save our list parameters
							 | 
						
						
						
							| 
								
							 | 
							
								                \list{\csname\@itemitem\endcsname}{%
							 | 
						
						
						
							| 
								
							 | 
							
								                \@IEEErestorelistparams% override any list{} changes
							 | 
						
						
						
							| 
								
							 | 
							
								                                       % to our globals
							 | 
						
						
						
							| 
								
							 | 
							
								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEiedlistdecl% let user alter parameters
							 | 
						
						
						
							| 
								
							 | 
							
								                #1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                % If the user has requested not to use the
							 | 
						
						
						
							| 
								
							 | 
							
								                % labelindent factor, don't revise \labelindent
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnolabelindentfactor\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEElabelindent=\IEEElabelindentfactor\labelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								                % Unless the user has requested otherwise,
							 | 
						
						
						
							| 
								
							 | 
							
								                % calculate our left margin based
							 | 
						
						
						
							| 
								
							 | 
							
								                % on \IEEElabelindent, \labelwidth and
							 | 
						
						
						
							| 
								
							 | 
							
								                % \labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnocalcleftmargin\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEEcalcleftmargin{\IEEElabelindent}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi}\fi\fi}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
							 | 
						
						
						
							| 
								
							 | 
							
								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran enumerate list MDS 1/2001
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here, shield end of lines with %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEenumerate[#1]{%
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifnum\@enumdepth>3\relax\@toodeep\else%
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifnum\@listdepth>5\relax\@toodeep\else%
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@enumdepth\@ne%
							 | 
						
						
						
							| 
								
							 | 
							
								                \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
							 | 
						
						
						
							| 
								
							 | 
							
								                % get the labelindentfactor for this level
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth\@ne% we need to know what the level WILL be
							 | 
						
						
						
							| 
								
							 | 
							
								                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth-\@ne% undo our increment
							 | 
						
						
						
							| 
								
							 | 
							
								                \def\@IEEEiedjustify{2}% right justified labels are default
							 | 
						
						
						
							| 
								
							 | 
							
								                % set other defaults
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnocalcleftmarginfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnolabelindentfactorfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \topsep\IEEEiedtopsep%
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEElabelindent\IEEEelabelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                \labelsep\IEEEiednormlabelsep%
							 | 
						
						
						
							| 
								
							 | 
							
								                \partopsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \parsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \rightmargin 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \listparindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                % calculate the label width
							 | 
						
						
						
							| 
								
							 | 
							
								                % We'll set it to the width suitable for all labels using
							 | 
						
						
						
							| 
								
							 | 
							
								                % normalfont 1) to 9)
							 | 
						
						
						
							| 
								
							 | 
							
								                % The user can override this later
							 | 
						
						
						
							| 
								
							 | 
							
								                \settowidth{\labelwidth}{9)}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \@IEEEsavelistparams% save our list parameters
							 | 
						
						
						
							| 
								
							 | 
							
								                \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \@IEEErestorelistparams% override any list{} changes
							 | 
						
						
						
							| 
								
							 | 
							
								                                       % to our globals
							 | 
						
						
						
							| 
								
							 | 
							
								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEiedlistdecl% let user alter parameters 
							 | 
						
						
						
							| 
								
							 | 
							
								                #1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                % If the user has requested not to use the
							 | 
						
						
						
							| 
								
							 | 
							
								                % IEEElabelindent factor, don't revise \IEEElabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnolabelindentfactor\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								                % Unless the user has requested otherwise,
							 | 
						
						
						
							| 
								
							 | 
							
								                % calculate our left margin based
							 | 
						
						
						
							| 
								
							 | 
							
								                % on \IEEElabelindent, \labelwidth and
							 | 
						
						
						
							| 
								
							 | 
							
								                % \labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnocalcleftmargin\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEEcalcleftmargin{\IEEElabelindent}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi}\fi\fi}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS
							 | 
						
						
						
							| 
								
							 | 
							
								% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran description list MDS 1/2001
							 | 
						
						
						
							| 
								
							 | 
							
								% Note controlled spacing here, shield end of lines with %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEdescription[#1]{%
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifnum\@listdepth>5\relax\@toodeep\else%
							 | 
						
						
						
							| 
								
							 | 
							
								                % get the labelindentfactor for this level
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth\@ne% we need to know what the level WILL be
							 | 
						
						
						
							| 
								
							 | 
							
								                \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \advance\@listdepth-\@ne% undo our increment
							 | 
						
						
						
							| 
								
							 | 
							
								                \def\@IEEEiedjustify{0}% left justified labels are default
							 | 
						
						
						
							| 
								
							 | 
							
								                % set other defaults
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnocalcleftmarginfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEnolabelindentfactorfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								                \topsep\IEEEiedtopsep% 
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEElabelindent\IEEEdlabelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                % assume normal labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								                \labelsep\IEEEiednormlabelsep%
							 | 
						
						
						
							| 
								
							 | 
							
								                \partopsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \parsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemsep 0ex%
							 | 
						
						
						
							| 
								
							 | 
							
								                \rightmargin 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \listparindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                \itemindent 0em%
							 | 
						
						
						
							| 
								
							 | 
							
								                % Bogus label width in case the user forgets
							 | 
						
						
						
							| 
								
							 | 
							
								                % to set it.
							 | 
						
						
						
							| 
								
							 | 
							
								                % TIP: If you want to see what a variable's width is you
							 | 
						
						
						
							| 
								
							 | 
							
								                % can use the TeX command \showthe\width-variable to 
							 | 
						
						
						
							| 
								
							 | 
							
								                % display it on the screen during compilation 
							 | 
						
						
						
							| 
								
							 | 
							
								                % (This might be helpful to know when you need to find out
							 | 
						
						
						
							| 
								
							 | 
							
								                % which label is the widest)
							 | 
						
						
						
							| 
								
							 | 
							
								                \settowidth{\labelwidth}{Hello}%
							 | 
						
						
						
							| 
								
							 | 
							
								                \@IEEEsavelistparams% save our list parameters
							 | 
						
						
						
							| 
								
							 | 
							
								                \list{}{\@IEEErestorelistparams% override any list{} changes
							 | 
						
						
						
							| 
								
							 | 
							
								                                               % to our globals
							 | 
						
						
						
							| 
								
							 | 
							
								                \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel
							 | 
						
						
						
							| 
								
							 | 
							
								                \IEEEiedlistdecl% let user alter parameters 
							 | 
						
						
						
							| 
								
							 | 
							
								                #1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                % If the user has requested not to use the
							 | 
						
						
						
							| 
								
							 | 
							
								                % labelindent factor, don't revise \IEEElabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnolabelindentfactor\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								                % Unless the user has requested otherwise,
							 | 
						
						
						
							| 
								
							 | 
							
								                % calculate our left margin based
							 | 
						
						
						
							| 
								
							 | 
							
								                % on \IEEElabelindent, \labelwidth and
							 | 
						
						
						
							| 
								
							 | 
							
								                % \labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								                \ifIEEEnocalcleftmargin\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \else\IEEEcalcleftmargin{\IEEElabelindent}\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								                \fi}\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.6b we use one makelabel that does justification as needed.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\makebox[\labelwidth][l]{\normalfont #1}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEiedjustify 1\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\makebox[\labelwidth][c]{\normalfont #1}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% VERSE and QUOTE
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 define environments with newenvironment
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{verse}{\let\\=\@centercr
							 | 
						
						
						
							| 
								
							 | 
							
								    \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent
							 | 
						
						
						
							| 
								
							 | 
							
								    \rightmargin\leftmargin\advance\leftmargin 1.5em}\item\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								    {\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{quotation}{\list{}{\listparindent 1.5em \itemindent\listparindent
							 | 
						
						
						
							| 
								
							 | 
							
								    \rightmargin\leftmargin \parsep 0pt plus 1pt}\item\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								    {\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{quote}{\list{}{\rightmargin\leftmargin}\item\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								    {\endlist}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \titlepage
							 | 
						
						
						
							| 
								
							 | 
							
								% provided only for backward compatibility. \maketitle is the correct
							 | 
						
						
						
							| 
								
							 | 
							
								% way to create the title page. 
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@restonecol
							 | 
						
						
						
							| 
								
							 | 
							
								\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
							 | 
						
						
						
							| 
								
							 | 
							
								    \else \newpage \fi \thispagestyle{empty}\c@page\z@}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% standard values from article.cls
							 | 
						
						
						
							| 
								
							 | 
							
								\arraycolsep     5pt
							 | 
						
						
						
							| 
								
							 | 
							
								\arrayrulewidth .4pt
							 | 
						
						
						
							| 
								
							 | 
							
								\doublerulesep   2pt
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\tabcolsep       6pt
							 | 
						
						
						
							| 
								
							 | 
							
								\tabbingsep      0.5em
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% FOOTNOTES
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								%\skip\footins 10pt plus 4pt minus 2pt
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 respond to changes in font size
							 | 
						
						
						
							| 
								
							 | 
							
								% space added above the footnotes (if present)
							 | 
						
						
						
							| 
								
							 | 
							
								\skip\footins 0.9\baselineskip  plus 0.4\baselineskip  minus 0.2\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6, we need to make \footnotesep responsive to changes
							 | 
						
						
						
							| 
								
							 | 
							
								% in \baselineskip or strange spacings will result when in
							 | 
						
						
						
							| 
								
							 | 
							
								% draft mode. Here is a little LaTeX secret - \footnotesep
							 | 
						
						
						
							| 
								
							 | 
							
								% determines the height of an invisible strut that is placed
							 | 
						
						
						
							| 
								
							 | 
							
								% *above* the baseline of footnotes after the first. Since
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX considers the space for characters to be 0.7/baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% above the baseline and 0.3/baselineskip below it, we need to
							 | 
						
						
						
							| 
								
							 | 
							
								% use 0.7/baselineskip as a \footnotesep to maintain equal spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% between all the lines of the footnotes. IEEE often uses a tad
							 | 
						
						
						
							| 
								
							 | 
							
								% more, so use 0.8\baselineskip. This slightly larger value also helps
							 | 
						
						
						
							| 
								
							 | 
							
								% the text to clear the footnote marks. Note that \thanks in IEEEtran
							 | 
						
						
						
							| 
								
							 | 
							
								% uses its own value of \footnotesep which is set in \maketitle.
							 | 
						
						
						
							| 
								
							 | 
							
								{\footnotesize
							 | 
						
						
						
							| 
								
							 | 
							
								\global\footnotesep 0.8\baselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\skip\@mpfootins = \skip\footins
							 | 
						
						
						
							| 
								
							 | 
							
								\fboxsep = 3pt
							 | 
						
						
						
							| 
								
							 | 
							
								\fboxrule = .4pt
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 use 1em, then use LaTeX2e's \@makefnmark
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that IEEE normally *left* aligns the footnote marks, so we don't need
							 | 
						
						
						
							| 
								
							 | 
							
								% box resizing tricks here.
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc does not use superscipts for footnote marks
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEcompsocmakefnmark{\hbox{\normalfont\@thefnmark.\ }}
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@IEEEcompsocmakefnmark}#1}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE does not use footnote rules
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnoterule{}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 for compsoc, IEEE uses a footnote rule only for \thanks. We devise a "one-shot"
							 | 
						
						
						
							| 
								
							 | 
							
								% system to implement this.
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEenableoneshotfootnoterule
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEenableoneshotfootnoterulefalse
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footnoterule{\relax\if@IEEEenableoneshotfootnoterule
							 | 
						
						
						
							| 
								
							 | 
							
								\kern-5pt
							 | 
						
						
						
							| 
								
							 | 
							
								\hbox to \columnwidth{\hfill\vrule width 0.5\columnwidth height 0.4pt\hfill}
							 | 
						
						
						
							| 
								
							 | 
							
								\kern4.6pt
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEenableoneshotfootnoterulefalse
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 do not allow LaTeX to break a footnote across multiple pages
							 | 
						
						
						
							| 
								
							 | 
							
								\interfootnotelinepenalty=10000
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 discourage breaks within equations
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that amsmath normally sets this to 10000,
							 | 
						
						
						
							| 
								
							 | 
							
								% but LaTeX2e normally uses 100.
							 | 
						
						
						
							| 
								
							 | 
							
								\interdisplaylinepenalty=2500
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% default allows section depth up to /paragraph
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{secnumdepth}{4}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% technotes do not allow /paragraph
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote
							 | 
						
						
						
							| 
								
							 | 
							
								   \setcounter{secnumdepth}{3}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% neither do compsoc conferences
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocconfonly{\setcounter{secnumdepth}{3}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{section}
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{subsection}[section]
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{subsubsection}[subsection]
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{paragraph}[subsubsection]
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% used only by IEEEtran's IEEEeqnarray as other packages may
							 | 
						
						
						
							| 
								
							 | 
							
								% have their own, different, implementations
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{IEEEsubequation}[equation]
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% as shown when called by user from \ref, \label and in table of contents
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theequation{\arabic{equation}}                          % 1
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}}  % 1a (used only by IEEEtran's IEEEeqnarray)
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc is all arabic
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesection{\arabic{section}}                
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesubsection{\thesection.\arabic{subsection}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesubsubsection{\thesubsection.\arabic{subsubsection}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theparagraph{\thesubsubsection.\arabic{paragraph}}
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesection{\Roman{section}}                             % I
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7, \mbox prevents breaks around - 
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesubsection{\mbox{\thesection-\Alph{subsection}}}     % I-A
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 use I-A1 format used by IEEE rather than I-A.1
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thesubsubsection{\thesubsection\arabic{subsubsection}}  % I-A1
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theparagraph{\thesubsubsection\alph{paragraph}}         % I-A1a
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% From Heiko Oberdiek. Because of the \mbox in \thesubsection, we need to
							 | 
						
						
						
							| 
								
							 | 
							
								% tell hyperref to disable the \mbox command when making PDF bookmarks.
							 | 
						
						
						
							| 
								
							 | 
							
								% This done already with hyperref.sty version 6.74o and later, but
							 | 
						
						
						
							| 
								
							 | 
							
								% it will not hurt to do it here again for users of older versions.
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifundefined{pdfstringdefPreHook}{\let\pdfstringdefPreHook\@empty}{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\g@addto@macro\pdfstringdefPreHook{\let\mbox\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Main text forms (how shown in main text headings)
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6, using \thesection in \thesectiondis allows changes
							 | 
						
						
						
							| 
								
							 | 
							
								% in the former to automatically appear in the latter
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifCLASSOPTIONconference% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesectiondis{\thesection.}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesubsectiondis{\thesectiondis\arabic{subsection}.}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesubsubsectiondis{\thesubsectiondis\arabic{subsubsection}.}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\theparagraphdis{\thesubsubsectiondis\arabic{paragraph}.}
							 | 
						
						
						
							| 
								
							 | 
							
								  \else% compsoc not conferencs
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesectiondis{\thesection}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesubsectiondis{\thesectiondis.\arabic{subsection}}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\thesubsubsectiondis{\thesubsectiondis.\arabic{subsubsection}}
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\theparagraphdis{\thesubsubsectiondis.\arabic{paragraph}}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\else% not compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\thesectiondis{\thesection.}                   % I.
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\thesubsectiondis{\Alph{subsection}.}          % B.
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\thesubsubsectiondis{\arabic{subsubsection})}  % 3)
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\theparagraphdis{\alph{paragraph})}            % d)
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% just like LaTeX2e's \@eqnnum
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEsubequation used only by IEEEtran's IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)
							 | 
						
						
						
							| 
								
							 | 
							
								% redirect LaTeX2e's equation number display and all that depend on
							 | 
						
						
						
							| 
								
							 | 
							
								% it, through IEEEtran's \theequationdis
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@eqnnum{\theequationdis}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 provide string macros as article.cls does
							 | 
						
						
						
							| 
								
							 | 
							
								\def\contentsname{Contents}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\listfigurename{List of Figures}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\listtablename{List of Tables}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\refname{References}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\indexname{Index}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\figurename{Fig.}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tablename{TABLE}
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocconfonly{\def\figurename{Figure}\def\tablename{Table}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\partname{Part}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\appendixname{Appendix}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\abstractname{Abstract}
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE specific names
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEkeywordsname{Index Terms}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEproofname{Proof}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@pnumwidth{1.55em}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@tocrmarg{2.55em}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@dotsep{4.5}
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{tocdepth}{3}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% adjusted some spacings here so that section numbers will not easily 
							 | 
						
						
						
							| 
								
							 | 
							
								% collide with the section titles. 
							 | 
						
						
						
							| 
								
							 | 
							
								% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.
							 | 
						
						
						
							| 
								
							 | 
							
								% MDS 1/2001
							 | 
						
						
						
							| 
								
							 | 
							
								\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%
							 | 
						
						
						
							| 
								
							 | 
							
								    \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%
							 | 
						
						
						
							| 
								
							 | 
							
								    \endgroup}
							 | 
						
						
						
							| 
								
							 | 
							
								% argument format #1:level, #2:labelindent,#3:labelsep
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}
							 | 
						
						
						
							| 
								
							 | 
							
								% must provide \l@ defs for ALL sublevels EVEN if tocdepth
							 | 
						
						
						
							| 
								
							 | 
							
								% is such as they will not appear in the table of contents
							 | 
						
						
						
							| 
								
							 | 
							
								% these defs are how TOC knows what level these things are!
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\listoffigures{\section*{\listfigurename}\@starttoc{lof}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\listoftables{\section*{\listtablename}\@starttoc{lot}}
							 | 
						
						
						
							| 
								
							 | 
							
								\let\l@table\l@figure
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% Definitions for floats
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Normal Floats
							 | 
						
						
						
							| 
								
							 | 
							
								\floatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\textfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\@fptop 0pt plus 1fil
							 | 
						
						
						
							| 
								
							 | 
							
								\@fpsep 0.75\baselineskip plus 2fil 
							 | 
						
						
						
							| 
								
							 | 
							
								\@fpbot 0pt plus 1fil
							 | 
						
						
						
							| 
								
							 | 
							
								\def\topfraction{0.9}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\bottomfraction{0.4}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\floatpagefraction{0.8}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7, let top floats approach 90% of page
							 | 
						
						
						
							| 
								
							 | 
							
								\def\textfraction{0.1}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% Double Column Floats
							 | 
						
						
						
							| 
								
							 | 
							
								\dblfloatsep 1\baselineskip plus  0.2\baselineskip minus  0.2\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\dbltextfloatsep 1.7\baselineskip plus  0.2\baselineskip minus  0.4\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that it would be nice if the rubber here actually worked in LaTeX2e.
							 | 
						
						
						
							| 
								
							 | 
							
								% There is a long standing limitation in LaTeX, first discovered (to the best
							 | 
						
						
						
							| 
								
							 | 
							
								% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable
							 | 
						
						
						
							| 
								
							 | 
							
								% portion of \dbltextfloatsep, and as a result, double column figures can and
							 | 
						
						
						
							| 
								
							 | 
							
								% do result in an non-integer number of lines in the main text columns with
							 | 
						
						
						
							| 
								
							 | 
							
								% underfull vbox errors as a consequence. A post to comp.text.tex
							 | 
						
						
						
							| 
								
							 | 
							
								% by Donald Arseneau confirms that this had not yet been fixed in 1998.
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't
							 | 
						
						
						
							| 
								
							 | 
							
								% protect you from other double floats. Happy vspace'ing.
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\@dblfptop 0pt plus 1fil
							 | 
						
						
						
							| 
								
							 | 
							
								\@dblfpsep 0.75\baselineskip plus 2fil
							 | 
						
						
						
							| 
								
							 | 
							
								\@dblfpbot 0pt plus 1fil
							 | 
						
						
						
							| 
								
							 | 
							
								\def\dbltopfraction{0.8}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\dblfloatpagefraction{0.8}
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{dbltopnumber}{4}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\intextsep 1\baselineskip plus 0.2\baselineskip minus  0.2\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{topnumber}{2}
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{bottomnumber}{2}
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{totalnumber}{4}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% article class provides these, we should too.
							 | 
						
						
						
							| 
								
							 | 
							
								\newlength\abovecaptionskip
							 | 
						
						
						
							| 
								
							 | 
							
								\newlength\belowcaptionskip
							 | 
						
						
						
							| 
								
							 | 
							
								% but only \abovecaptionskip is used above figure captions and *below* table
							 | 
						
						
						
							| 
								
							 | 
							
								% captions
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength\abovecaptionskip{0.5\baselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength\belowcaptionskip{0pt}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 create hooks in case the caption spacing ever needs to be
							 | 
						
						
						
							| 
								
							 | 
							
								% overridden by a user
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% 1.6b revise caption system so that \@makecaption uses two arguments
							 | 
						
						
						
							| 
								
							 | 
							
								% as with LaTeX2e. Otherwise, there will be problems when using hyperref.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtablestring{table}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc \@makecaption
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makecaption#1#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								% test if is a for a figure or table
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@captype\@IEEEtablestring%
							 | 
						
						
						
							| 
								
							 | 
							
								% if a table, do table caption
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize\begin{center}{\normalfont\sffamily\normalsize {#1.}~ #2}\end{center}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtablecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								% if not a table, format it as a figure
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEfigurecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim \wd\@tempboxa >\hsize%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is longer than a line, let it wrap around
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
							 | 
						
						
						
							| 
								
							 | 
							
								\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is shorter than a line, center
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\hbox to\hsize{\normalfont\sffamily\normalsize\hfil\box\@tempboxa\hfil}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								\else% nonconference compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makecaption#1#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								% test if is a for a figure or table
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@captype\@IEEEtablestring%
							 | 
						
						
						
							| 
								
							 | 
							
								% if a table, do table caption
							 | 
						
						
						
							| 
								
							 | 
							
								\normalsize\begin{center}{\normalfont\sffamily\normalsize #1}\\{\normalfont\sffamily\normalsize #2}\end{center}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtablecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								% if not a table, format it as a figure
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEfigurecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ #2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim \wd\@tempboxa >\hsize%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is longer than a line, let it wrap around
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}~ }%
							 | 
						
						
						
							| 
								
							 | 
							
								\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is shorter than a line, left justify
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\hbox to\hsize{\normalfont\sffamily\normalsize\box\@tempboxa\hfil}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\else% traditional noncompsoc \@makecaption
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makecaption#1#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								% test if is a for a figure or table
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@captype\@IEEEtablestring%
							 | 
						
						
						
							| 
								
							 | 
							
								% if a table, do table caption
							 | 
						
						
						
							| 
								
							 | 
							
								\footnotesize\begin{center}{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\end{center}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtablecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								% if not a table, format it as a figure
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEfigurecaptionsepspace
							 | 
						
						
						
							| 
								
							 | 
							
								% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ #2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim \wd\@tempboxa >\hsize%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is longer than a line, let it wrap around
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}~~ }%
							 | 
						
						
						
							| 
								
							 | 
							
								\parbox[t]{\hsize}{\normalfont\footnotesize\noindent\unhbox\@tempboxa#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								% if caption is shorter than a line, center if conference, left justify otherwise
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference \hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else \hbox to\hsize{\normalfont\footnotesize\box\@tempboxa\hfil}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 disable captions class option, do so in a way that retains operation of \label
							 | 
						
						
						
							| 
								
							 | 
							
								% within \caption
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcaptionsoff
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@makecaption#1#2{\vspace*{2em}\footnotesize\begin{center}{\footnotesize #1}\end{center}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEtemporiglabeldefsave\label
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEtemplabelargsave\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\def\label##1{\gdef\@IEEEtemplabelargsave{##1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@tempboxa\hbox{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\label\@IEEEtemporiglabeldefsave
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEtemplabelargsave\relax\else\label{\@IEEEtemplabelargsave}\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 define end environments with \def not \let so as to work OK with
							 | 
						
						
						
							| 
								
							 | 
							
								% preview-latex
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{figure}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thefigure{\@arabic\c@figure}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\fps@figure{tbp}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ftype@figure{1}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ext@figure{lof}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\fnum@figure{\figurename~\thefigure}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\figure{\@float{figure}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endfigure{\end@float}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{figure*}{\@dblfloat{figure}}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endfigure*}{\end@dblfloat}
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{table}
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thetable{\arabic{table}}
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thetable{\@Roman\c@table}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\def\fps@table{tbp}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ftype@table{2}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ext@table{lot}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\fnum@table{\tablename~\thetable}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 IEEE uses 8pt text for tables
							 | 
						
						
						
							| 
								
							 | 
							
								% to default to footnotesize, we hack into LaTeX2e's \@floatboxreset and pray
							 | 
						
						
						
							| 
								
							 | 
							
								\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endtable{\end@float}
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.6b double column tables need to default to footnotesize as well.
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endtable*}{\end@dblfloat}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% START OF IEEEeqnarry DEFINITIONS
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% Inspired by the concepts, examples, and previous works of LaTeX 
							 | 
						
						
						
							| 
								
							 | 
							
								%% coders and developers such as Donald Arseneau, Fred Bartlett, 
							 | 
						
						
						
							| 
								
							 | 
							
								%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Roland Winkler and Mark Wooding.
							 | 
						
						
						
							| 
								
							 | 
							
								%% I don't make the claim that my work here is even near their calibre. ;)
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEclspkgerror{\ClassError{IEEEtran}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEeqnarraystarform% flag to indicate if the environment was called as the star form
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraystarformfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter
							 | 
						
						
						
							| 
								
							 | 
							
								% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								% used by IEEEeqnarraymulticol so that it can work properly in both
							 | 
						
						
						
							| 
								
							 | 
							
								\@advanceIEEEeqncolcnttrue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined
							 | 
						
						
						
							| 
								
							 | 
							
								\newcount\@IEEEeqncolcnt  % tracks how many IEEEeqnarray cols the user actually used
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% The default math style used by the columns
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraymathstyle{\displaystyle}
							 | 
						
						
						
							| 
								
							 | 
							
								% The default text style used by the columns
							 | 
						
						
						
							| 
								
							 | 
							
								% default to using the current font
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraytextstyle{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% like the iedlistdecl but for \IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraydecl{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayboxdecl{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \yesnumber is the opposite of \nonumber
							 | 
						
						
						
							| 
								
							 | 
							
								% a novel concept with the same def as the equationarray package
							 | 
						
						
						
							| 
								
							 | 
							
								% However, we give IEEE versions too since some LaTeX packages such as 
							 | 
						
						
						
							| 
								
							 | 
							
								% the MDWtools mathenv.sty redefine \nonumber to something else.
							 | 
						
						
						
							| 
								
							 | 
							
								\providecommand{\yesnumber}{\global\@eqnswtrue}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEyesnumber{\global\@eqnswtrue}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEnonumber{\global\@eqnswfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEyessubnumber{\global\@IEEEissubequationtrue\global\@eqnswtrue%
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayISinner% only do something inside an IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEElastlinewassubequation\addtocounter{equation}{-1}\else\setcounter{IEEEsubequation}{1}\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flag to indicate that an equation is a sub equation
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEissubequation%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEissubequationfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% allows users to "push away" equations that get too close to the equation numbers
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraynumspace{\hphantom{\if@IEEEissubequation\theIEEEsubequationdis\else\theequationdis\fi}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provides a way to span multiple columns within IEEEeqnarray environments
							 | 
						
						
						
							| 
								
							 | 
							
								% will consider \if@advanceIEEEeqncolcnt before globally advancing the
							 | 
						
						
						
							| 
								
							 | 
							
								% column counter - so as to work within \IEEEeqnarraybox
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								% check if column is defined
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined%
							 | 
						
						
						
							| 
								
							 | 
							
								\csname @IEEEeqnarraycolPRE#2\endcsname#3\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST#2\endcsname%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% if not, error and use default type
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								Using a default centering column instead}%
							 | 
						
						
						
							| 
								
							 | 
							
								{You must define IEEEeqnarray column types before use.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname#3\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% like \omit, but maintains track of the column counter for \IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provides a way to define a letter referenced column type
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provides a way to define a numerically referenced inter-column glue types
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% expands and appends the given argument to the \@IEEEtrantmptoksA token list
							 | 
						
						
						
							| 
								
							 | 
							
								% used to build up the \halign preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@@IEEEappendtoksA}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% also appends to \@IEEEtrantmptoksA, but does not expand the argument
							 | 
						
						
						
							| 
								
							 | 
							
								% uses \toks8 as a scratchpad register
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@@IEEEappendNOEXPANDtoksA}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% define some common column types for the user
							 | 
						
						
						
							| 
								
							 | 
							
								% math
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}
							 | 
						
						
						
							| 
								
							 | 
							
								% text
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% vertical rules
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% horizontal rules
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% plain
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{x}{}{}
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{X}{$}{$}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% the default column type to use in the event a column type is not defined
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% a zero tabskip (used for "-" col types)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}
							 | 
						
						
						
							| 
								
							 | 
							
								% a centering tabskip (used for "+" col types)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% top level default tabskip glues for the start, end, and inter-column
							 | 
						
						
						
							| 
								
							 | 
							
								% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% creates a vertical rule that extends from the bottom to the top a a cell
							 | 
						
						
						
							| 
								
							 | 
							
								% Provided in case other packages redefine \vline some other way.
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarrayvrule[rule thickness]
							 | 
						
						
						
							| 
								
							 | 
							
								% If no argument is provided, \arrayrulewidth will be used for the rule thickness. 
							 | 
						
						
						
							| 
								
							 | 
							
								\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% creates a blank separator row
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarrayseprow[separation length][font size commands]
							 | 
						
						
						
							| 
								
							 | 
							
								% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]
							 | 
						
						
						
							| 
								
							 | 
							
								% blank arguments inherit the default values
							 | 
						
						
						
							| 
								
							 | 
							
								% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarrayseprowARGONE\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								% get the skip value, based on the font commands
							 | 
						
						
						
							| 
								
							 | 
							
								% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
							 | 
						
						
						
							| 
								
							 | 
							
								% assign within a bogus box to confine the font changes
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% creates a blank separator row, but omits all the column templates
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]
							 | 
						
						
						
							| 
								
							 | 
							
								% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]
							 | 
						
						
						
							| 
								
							 | 
							
								% blank arguments inherit the default values
							 | 
						
						
						
							| 
								
							 | 
							
								% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarrayseprowARGONE\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								% get the skip value, based on the font commands
							 | 
						
						
						
							| 
								
							 | 
							
								% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3
							 | 
						
						
						
							| 
								
							 | 
							
								% assign within a bogus box to confine the font changes
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#2\relax\global\skip5=#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% draws a single rule across all the columns optional
							 | 
						
						
						
							| 
								
							 | 
							
								% argument determines the rule width, \arrayrulewidth is the default
							 | 
						
						
						
							| 
								
							 | 
							
								% updates column counter as needed and turns off struts
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarrayrulerow[rule line thickness]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule 
							 | 
						
						
						
							| 
								
							 | 
							
								% turn off any struts
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% draws a double rule by using a single rule row, a separator row, and then
							 | 
						
						
						
							| 
								
							 | 
							
								% another single rule row 
							 | 
						
						
						
							| 
								
							 | 
							
								% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
							 | 
						
						
						
							| 
								
							 | 
							
								% second optional argument determines the rule spacing, \doublerulesep is the default
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								% we allow the user to say \IEEEeqnarraydblrulerow[][]
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[\arrayrulewidth]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[#1]\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerowARG{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\IEEEeqnarrayseprow[#2][\relax]%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\multispan{\@IEEEeqnnumcols}%
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerowARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[\arrayrulewidth]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[#1]%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% draws a double rule by using a single rule row, a separator (cutting) row, and then
							 | 
						
						
						
							| 
								
							 | 
							
								% another single rule row 
							 | 
						
						
						
							| 
								
							 | 
							
								% first optional argument determines the rule thicknesses, \arrayrulewidth is the default
							 | 
						
						
						
							| 
								
							 | 
							
								% second optional argument determines the rule spacing, \doublerulesep is the default
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								% we allow the user to say \IEEEeqnarraydblrulerow[][]
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[\arrayrulewidth]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[#1]%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerowARG{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\IEEEeqnarrayseprowcut[#2][\relax]%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\\\multispan{\@IEEEeqnnumcols}%
							 | 
						
						
						
							| 
								
							 | 
							
								% advance column counter only if the IEEEeqnarray environment wants it
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraydblrulerowARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraydblrulerowARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[\arrayrulewidth]%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayrulerow[#1]%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% inserts a full row's worth of &'s
							 | 
						
						
						
							| 
								
							 | 
							
								% relies on \@IEEEeqnnumcols to provide the correct number of columns
							 | 
						
						
						
							| 
								
							 | 
							
								% uses \@IEEEtrantmptoksA, \count0 as scratch registers
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\loop% add cols if the user did not use them all
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum\count0<\@IEEEeqnnumcols\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{&}%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\count0 by 1\relax% update the col count
							 | 
						
						
						
							| 
								
							 | 
							
								\repeat%
							 | 
						
						
						
							| 
								
							 | 
							
								\the\@IEEEtrantmptoksA%execute the &'s
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayISinnerfalse    % of an IEEEeqnarray - after the IEEEeqnarraydecl
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutdepth{0pt}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt}  % struts within an IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayusemasterstruttrue     % is to be used
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% saves the strut height and depth of the master strut
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraymasterstrutsave{\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% save values
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% restores the strut height and depth of the master strut
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraymasterstrutrestore{\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% restore values
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% globally restores the strut height and depth to the 
							 | 
						
						
						
							| 
								
							 | 
							
								% master values and sets the master strut flag to true
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraystrutreset{\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% restore values
							 | 
						
						
						
							| 
								
							 | 
							
								\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEeqnarrayusemasterstruttrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% if the master strut is not to be used, make the current
							 | 
						
						
						
							| 
								
							 | 
							
								% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth
							 | 
						
						
						
							| 
								
							 | 
							
								% and the use master strut flag, global
							 | 
						
						
						
							| 
								
							 | 
							
								% this allows user strut commands issued in the last column to be carried
							 | 
						
						
						
							| 
								
							 | 
							
								% into the isolation/strut column
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayglobalizestrutstatus{\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayusemasterstrut\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%
							 | 
						
						
						
							| 
								
							 | 
							
								\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEeqnarrayusemasterstrutfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]
							 | 
						
						
						
							| 
								
							 | 
							
								% If called outside the lines of an IEEEeqnarray, sets the height
							 | 
						
						
						
							| 
								
							 | 
							
								% and depth of both the master and local struts. If called inside
							 | 
						
						
						
							| 
								
							 | 
							
								% an IEEEeqnarray line, sets the height and depth of the local strut
							 | 
						
						
						
							| 
								
							 | 
							
								% only and sets the flag to indicate the use of the local strut
							 | 
						
						
						
							| 
								
							 | 
							
								% values. If the height or depth is left blank, 0.7\normalbaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% and 0.3\normalbaselineskip will be used, respectively.
							 | 
						
						
						
							| 
								
							 | 
							
								% The optional argument can be used to evaluate the lengths under
							 | 
						
						
						
							| 
								
							 | 
							
								% a different font size and styles. If none is specified, the current
							 | 
						
						
						
							| 
								
							 | 
							
								% font is used.
							 | 
						
						
						
							| 
								
							 | 
							
								% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraystrutsizeARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% arg one present
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% if null arg
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraystrutsizeARG{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraystrutsizeARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% arg two present
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% if null arg
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability, just to be safe
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% dimen0 = height, dimen2 = depth
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayISinner% inner does not touch master strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayusemasterstrutfalse% do not use master
							 | 
						
						
						
							| 
								
							 | 
							
								\else% outer, have to set master strut too
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayusemasterstruttrue% use master strut
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]
							 | 
						
						
						
							| 
								
							 | 
							
								% If called outside the lines of an IEEEeqnarray, adds the given height
							 | 
						
						
						
							| 
								
							 | 
							
								% and depth to both the master and local struts.
							 | 
						
						
						
							| 
								
							 | 
							
								% If called inside an IEEEeqnarray line, adds the given height and depth
							 | 
						
						
						
							| 
								
							 | 
							
								% to the local strut only and sets the flag to indicate the use 
							 | 
						
						
						
							| 
								
							 | 
							
								% of the local strut values.
							 | 
						
						
						
							| 
								
							 | 
							
								% In both cases, if a height or depth is left blank, 0pt is used instead.
							 | 
						
						
						
							| 
								
							 | 
							
								% The optional argument can be used to evaluate the lengths under
							 | 
						
						
						
							| 
								
							 | 
							
								% a different font size and styles. If none is specified, the current
							 | 
						
						
						
							| 
								
							 | 
							
								% font is used.
							 | 
						
						
						
							| 
								
							 | 
							
								% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraystrutsizearg\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% arg one present
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% if null arg
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraystrutsizearg{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEeqnarraystrutsizearg\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% arg two present
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{#3\relax\global\skip3=#2}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=\skip3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% if null arg
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability, just to be safe
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% dimen0 = height, dimen2 = depth
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayISinner% inner does not touch master strut size
							 | 
						
						
						
							| 
								
							 | 
							
								% get local strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% add it to the user supplied values
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\dimen0 by \skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\dimen2 by \skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% update the local strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayusemasterstrutfalse% do not use master
							 | 
						
						
						
							| 
								
							 | 
							
								\else% outer, have to set master strut too
							 | 
						
						
						
							| 
								
							 | 
							
								% get master strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% add it to the user supplied values
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\dimen0 by \skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\dimen2 by \skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% update the local and master strut sizes
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayusemasterstruttrue% use master strut
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% allow user a way to see the struts
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\ifIEEEvisiblestruts
							 | 
						
						
						
							| 
								
							 | 
							
								\IEEEvisiblestrutsfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% inserts an invisible strut using the master or local strut values
							 | 
						
						
						
							| 
								
							 | 
							
								% uses scratch registers \skip0, \skip2, \dimen0, \dimen2
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayinsertstrut{\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayusemasterstrut
							 | 
						
						
						
							| 
								
							 | 
							
								% get master strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								% get local strut size
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability, probably not needed
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% dimen0 = height, dimen2 = depth
							 | 
						
						
						
							| 
								
							 | 
							
								% allow user to see struts if desired
							 | 
						
						
						
							| 
								
							 | 
							
								\ifIEEEvisiblestruts%
							 | 
						
						
						
							| 
								
							 | 
							
								\vrule width0.2pt height\dimen0 depth\dimen2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\vrule width0pt height\dimen0 depth\dimen2\relax\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% creates an invisible strut, useable even outside \IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. 
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEstrut[height][depth][font size commands]
							 | 
						
						
						
							| 
								
							 | 
							
								% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]
							 | 
						
						
						
							| 
								
							 | 
							
								% blank arguments inherit the default values
							 | 
						
						
						
							| 
								
							 | 
							
								% uses \dimen0, \dimen2, \skip0, \skip2
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstrutARG{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEstrutARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=0.7\normalbaselineskip\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip0=#1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstrutARG{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEstrutARG\@empty%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=0.3\normalbaselineskip\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\skip2=#2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% remove stretchability, probably not needed
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen0\skip0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\dimen2\skip2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifIEEEvisiblestruts%
							 | 
						
						
						
							| 
								
							 | 
							
								\vrule width0.2pt height\dimen0 depth\dimen2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% enables strut mode by setting a default strut size and then zeroing the
							 | 
						
						
						
							| 
								
							 | 
							
								% \baselineskip, \lineskip, \lineskiplimit and \jot
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%
							 | 
						
						
						
							| 
								
							 | 
							
								\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarray{\@IEEEeqnarraystarformfalse\@IEEEeqnarray}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEeqnarray{\end@IEEEeqnarray}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{IEEEeqnarray*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarray}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarray is an enhanced \eqnarray. 
							 | 
						
						
						
							| 
								
							 | 
							
								% The star form defaults to not putting equation numbers at the end of each row.
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarray[decl]{cols}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarray[#1]#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								   % default to showing the equation number or not based on whether or not
							 | 
						
						
						
							| 
								
							 | 
							
								   % the star form was involked
							 | 
						
						
						
							| 
								
							 | 
							
								   \if@IEEEeqnarraystarform\global\@eqnswfalse
							 | 
						
						
						
							| 
								
							 | 
							
								   \else% not the star form
							 | 
						
						
						
							| 
								
							 | 
							
								   \global\@eqnswtrue
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi% if star form
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEissubequationfalse% default to no subequations
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEElastlinewassubequationfalse% assume last line is not a sub equation
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
							 | 
						
						
						
							| 
								
							 | 
							
								   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
							 | 
						
						
						
							| 
								
							 | 
							
								   % no extra space unless the user specifically requests it
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskip=0pt\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskiplimit=0pt\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   \baselineskip=\normalbaselineskip\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \jot=\IEEEnormaljot\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \mathsurround\z@\relax% no extra spacing around math
							 | 
						
						
						
							| 
								
							 | 
							
								   \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, 
							 | 
						
						
						
							| 
								
							 | 
							
								                             % used in \IEEEeqnarraymulticol and in the preamble build
							 | 
						
						
						
							| 
								
							 | 
							
								   \stepcounter{equation}% advance equation counter before first line
							 | 
						
						
						
							| 
								
							 | 
							
								   \setcounter{IEEEsubequation}{0}% no subequation yet 
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@currentlabel{\p@equation\theequation}% redefine the ref label
							 | 
						
						
						
							| 
								
							 | 
							
								   \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides
							 | 
						
						
						
							| 
								
							 | 
							
								   #1\relax% allow user to override defaults
							 | 
						
						
						
							| 
								
							 | 
							
								   \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers
							 | 
						
						
						
							| 
								
							 | 
							
								   \global\@IEEEeqncolcnt\z@% col. count = 0 for first line
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEbuildpreamble #2\end\relax% build the preamble and put it into \@IEEEtrantmptoksA 
							 | 
						
						
						
							| 
								
							 | 
							
								   % put in the column for the equation number
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
							 | 
						
						
						
							| 
								
							 | 
							
								   \toks0={##}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % add the isolation column
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % add the equation number col to the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % note \@IEEEeqnnumcols does not count the equation col or isolation col
							 | 
						
						
						
							| 
								
							 | 
							
								   % set the starting tabskip glue as determined by the preamble build
							 | 
						
						
						
							| 
								
							 | 
							
								   \tabskip=\@IEEEBPstartglue\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   % begin the display alignment
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarrayISinnertrue% commands are now within the lines
							 | 
						
						
						
							| 
								
							 | 
							
								   $$\everycr{}\halign to\displaywidth\bgroup
							 | 
						
						
						
							| 
								
							 | 
							
								   % "exspand" the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								   \span\the\@IEEEtrantmptoksA\cr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% enter isolation/strut column (or the next column if the user did not use
							 | 
						
						
						
							| 
								
							 | 
							
								% every column), record the strut status, complete the columns, do the strut if needed,
							 | 
						
						
						
							| 
								
							 | 
							
								% restore counters to correct values and exit
							 | 
						
						
						
							| 
								
							 | 
							
								\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup%
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEElastlinewassubequation\global\advance\c@IEEEsubequation\m@ne\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\advance\c@equation\m@ne%
							 | 
						
						
						
							| 
								
							 | 
							
								$$\@ignoretrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% need a way to remember if last line is a subequation
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEElastlinewassubequation%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEElastlinewassubequationfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEeqnarray uses a modifed \\ instead of the plain \cr to
							 | 
						
						
						
							| 
								
							 | 
							
								% end rows. This allows for things like \\*[vskip amount]
							 | 
						
						
						
							| 
								
							 | 
							
								% This "cr" macros are modified versions those for LaTeX2e's eqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								% the {\ifnum0=`} braces must be kept away from the last column to avoid
							 | 
						
						
						
							| 
								
							 | 
							
								% altering spacing of its math, so we use & to advance to the next column
							 | 
						
						
						
							| 
								
							 | 
							
								% as there is an isolation/strut column after the user's columns
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column
							 | 
						
						
						
							| 
								
							 | 
							
								   {\ifnum0=`}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								   \@ifstar{%
							 | 
						
						
						
							| 
								
							 | 
							
								      \global\@eqpen\@M\@IEEEeqnarrayYCR
							 | 
						
						
						
							| 
								
							 | 
							
								   }{%
							 | 
						
						
						
							| 
								
							 | 
							
								      \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR
							 | 
						
						
						
							| 
								
							 | 
							
								   }%
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayXCR[#1]{%
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifnum0=`{\fi}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \@@IEEEeqnarraycr
							 | 
						
						
						
							| 
								
							 | 
							
								   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								                          environment}%
							 | 
						
						
						
							| 
								
							 | 
							
								    {Use fewer \string &'s or put more columns in the IEEEeqnarry column\MessageBreak 
							 | 
						
						
						
							| 
								
							 | 
							
								     specifications.}\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								    \loop% add cols if the user did not use them all
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEappendtoksA{&}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEeqncolcnt by 1\relax% update the col count
							 | 
						
						
						
							| 
								
							 | 
							
								    \repeat
							 | 
						
						
						
							| 
								
							 | 
							
								    % this number of &'s will take us the the isolation column
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    % execute the &'s
							 | 
						
						
						
							| 
								
							 | 
							
								    \the\@IEEEtrantmptoksA%
							 | 
						
						
						
							| 
								
							 | 
							
								    % handle the strut/isolation column
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEeqnarrayinsertstrut% do the strut if needed
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								    &% and enter the equation number column
							 | 
						
						
						
							| 
								
							 | 
							
								    % is this line needs an equation number, display it and advance the
							 | 
						
						
						
							| 
								
							 | 
							
								    % (sub)equation counters, record what type this line was
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@eqnsw%
							 | 
						
						
						
							| 
								
							 | 
							
								     \if@IEEEissubequation\theIEEEsubequationdis\addtocounter{equation}{1}\stepcounter{IEEEsubequation}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \global\@IEEElastlinewassubequationtrue%
							 | 
						
						
						
							| 
								
							 | 
							
								     \else% display a standard equation number, initialize the IEEEsubequation counter
							 | 
						
						
						
							| 
								
							 | 
							
								     \theequationdis\stepcounter{equation}\setcounter{IEEEsubequation}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \global\@IEEElastlinewassubequationfalse\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    % reset the eqnsw flag to indicate default preference of the display of equation numbers
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@IEEEeqnarraystarform\global\@eqnswfalse\else\global\@eqnswtrue\fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \global\@IEEEissubequationfalse% reset the subequation flag
							 | 
						
						
						
							| 
								
							 | 
							
								    % reset the number of columns the user actually used
							 | 
						
						
						
							| 
								
							 | 
							
								    \global\@IEEEeqncolcnt\z@\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    % the real end of the line
							 | 
						
						
						
							| 
								
							 | 
							
								    \cr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything
							 | 
						
						
						
							| 
								
							 | 
							
								% inside a vtop, vbox, or vcenter box depending on the letter in the second
							 | 
						
						
						
							| 
								
							 | 
							
								% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,
							 | 
						
						
						
							| 
								
							 | 
							
								% equation numbers are not displayed and \IEEEeqnarraybox can be nested.
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox
							 | 
						
						
						
							| 
								
							 | 
							
								% within an hbox.
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within
							 | 
						
						
						
							| 
								
							 | 
							
								% a \hbox{$ $} construct.
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or 
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEeqnarrayboxt depending on the math mode.
							 | 
						
						
						
							| 
								
							 | 
							
								% The third optional argument specifies the width this box is to be set to -
							 | 
						
						
						
							| 
								
							 | 
							
								% natural width is the default.
							 | 
						
						
						
							| 
								
							 | 
							
								% The * forms do not add \jot line spacing
							 | 
						
						
						
							| 
								
							 | 
							
								% usage: \IEEEeqnarraybox[decl][pos][width]{cols}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayboxm{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarrayboxt{\@IEEEeqnarraystarformfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarraystarformtrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEeqnarraybox{\@IEEEeqnarraystarformfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarraystarformtrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} 
							 | 
						
						
						
							| 
								
							 | 
							
								% for \vcenter in non-math mode
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEeqnarrayboxHBOXSW%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayboxHBOXSWfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarraymasterstrutsave% save current master strut values
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise
							 | 
						
						
						
							| 
								
							 | 
							
								   \IEEEvisiblestrutsfalse% diagnostic mode defaults to off
							 | 
						
						
						
							| 
								
							 | 
							
								   % no extra space unless the user specifically requests it
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskip=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskiplimit=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \baselineskip=\normalbaselineskip\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \jot=\IEEEnormaljot\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \mathsurround\z@\relax% no extra spacing around math
							 | 
						
						
						
							| 
								
							 | 
							
								   % the default end glues are zero for an \IEEEeqnarraybox
							 | 
						
						
						
							| 
								
							 | 
							
								   \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue
							 | 
						
						
						
							| 
								
							 | 
							
								   \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue
							 | 
						
						
						
							| 
								
							 | 
							
								   \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue
							 | 
						
						
						
							| 
								
							 | 
							
								   \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, 
							 | 
						
						
						
							| 
								
							 | 
							
								                              % used in \IEEEeqnarraymulticol and in the preamble build
							 | 
						
						
						
							| 
								
							 | 
							
								   \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides
							 | 
						
						
						
							| 
								
							 | 
							
								   #1\relax% allow user to override defaults
							 | 
						
						
						
							| 
								
							 | 
							
								   \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEbuildpreamble #4\end\relax% build the preamble and put it into \@IEEEtrantmptoksA
							 | 
						
						
						
							| 
								
							 | 
							
								   % add an isolation column to the preamble to stop \\'s {} from getting into the last col
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first
							 | 
						
						
						
							| 
								
							 | 
							
								   \toks0={##}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % add the isolation column to the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% 
							 | 
						
						
						
							| 
								
							 | 
							
								   % set the starting tabskip glue as determined by the preamble build
							 | 
						
						
						
							| 
								
							 | 
							
								   \tabskip=\@IEEEBPstartglue\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   % begin the alignment
							 | 
						
						
						
							| 
								
							 | 
							
								   \everycr{}%
							 | 
						
						
						
							| 
								
							 | 
							
								   % use only the very first token to determine the positioning
							 | 
						
						
						
							| 
								
							 | 
							
								   % this stops some problems when the user uses more than one letter,
							 | 
						
						
						
							| 
								
							 | 
							
								   % but is probably not worth the effort
							 | 
						
						
						
							| 
								
							 | 
							
								   % \noindent is used as a delimiter
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEgrabfirstoken#2\relax\relax\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								   % \@IEEEgrabbedfirstoken has the first token, the rest are discarded
							 | 
						
						
						
							| 
								
							 | 
							
								   % if we need to put things into and hbox and go into math mode, do so now
							 | 
						
						
						
							| 
								
							 | 
							
								   \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								   % use the appropriate vbox type
							 | 
						
						
						
							| 
								
							 | 
							
								   \if\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken c\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \vcenter\else\vbox\fi\fi\bgroup%
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEeqnarrayISinnertrue% commands are now within the lines
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifx#3\relax\halign\else\halign to #3\relax\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								   \bgroup
							 | 
						
						
						
							| 
								
							 | 
							
								   % "exspand" the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								   \span\the\@IEEEtrantmptoksA\cr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% carry strut status and enter the isolation/strut column, 
							 | 
						
						
						
							| 
								
							 | 
							
								% exit from math mode if needed, and exit
							 | 
						
						
						
							| 
								
							 | 
							
								\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
							 | 
						
						
						
							| 
								
							 | 
							
								&% enter isolation/strut column
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayinsertstrut% do strut if needed
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values
							 | 
						
						
						
							| 
								
							 | 
							
								% reset the strut system for next IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								% (sets local strut values back to previous master strut values)
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraystrutreset%
							 | 
						
						
						
							| 
								
							 | 
							
								% ensure last line, exit from halign, close vbox
							 | 
						
						
						
							| 
								
							 | 
							
								\crcr\egroup\egroup%
							 | 
						
						
						
							| 
								
							 | 
							
								% exit from math mode and close hbox if needed
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to
							 | 
						
						
						
							| 
								
							 | 
							
								% end rows. This allows for things like \\[vskip amount]
							 | 
						
						
						
							| 
								
							 | 
							
								% This "cr" macros are modified versions those for LaTeX2e's eqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								% For IEEEeqnarraybox, \\* is the same as \\
							 | 
						
						
						
							| 
								
							 | 
							
								% the {\ifnum0=`} braces must be kept away from the last column to avoid
							 | 
						
						
						
							| 
								
							 | 
							
								% altering spacing of its math, so we use & to advance to the isolation/strut column
							 | 
						
						
						
							| 
								
							 | 
							
								% carry strut status into isolation/strut column
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status
							 | 
						
						
						
							| 
								
							 | 
							
								&% enter isolation/strut column
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarrayinsertstrut% do strut if needed
							 | 
						
						
						
							| 
								
							 | 
							
								% reset the strut system for next line or IEEEeqnarray
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnarraystrutreset%
							 | 
						
						
						
							| 
								
							 | 
							
								{\ifnum0=`}\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% test and setup the optional argument to \\[]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEeqnarraybox does not automatically increase line spacing by \jot
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%
							 | 
						
						
						
							| 
								
							 | 
							
								\cr\noalign{\if@IEEEeqnarraystarform\else\vskip\jot\fi\vskip#1\relax}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% starts the halign preamble build
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEbuildpreamble{\@IEEEtrantmptoksA={}% clear token register
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurtype=u%current column type is not yet known
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPprevtype=s%the previous column type was the start
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPnexttype=u%next column type is not yet known
							 | 
						
						
						
							| 
								
							 | 
							
								% ensure these are valid
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition
							 | 
						
						
						
							| 
								
							 | 
							
								% currently acquired numerically referenced glue
							 | 
						
						
						
							| 
								
							 | 
							
								% use a name that is easier to remember
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEBPcurnum=0%
							 | 
						
						
						
							| 
								
							 | 
							
								% tracks number of columns in the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEeqnnumcols=0%
							 | 
						
						
						
							| 
								
							 | 
							
								% record the default end glues
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%
							 | 
						
						
						
							| 
								
							 | 
							
								% now parse the user's column specifications
							 | 
						
						
						
							| 
								
							 | 
							
								\@@IEEEbuildpreamble}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% parses and builds the halign preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%
							 | 
						
						
						
							| 
								
							 | 
							
								% use only the very first token to check the end
							 | 
						
						
						
							| 
								
							 | 
							
								% \noindent is used as a delimiter as \end can be present here
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEgrabfirstoken#1\relax\relax\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgrabbedfirstoken\end\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%
							 | 
						
						
						
							| 
								
							 | 
							
								% identify current and next token type
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next
							 | 
						
						
						
							| 
								
							 | 
							
								% if curtype is a glue, get the glue def
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% if curtype is a column, get the column def and set the current column name
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% if curtype is a numeral, acquire the user defined glue
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% process the acquired glue 
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% process the acquired col 
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% ready prevtype for next col spec.
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPprevtype=\@IEEEBPcurtype%
							 | 
						
						
						
							| 
								
							 | 
							
								% be sure and put back the future token(s) as a group
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\@@nextIEEEbuildpreamble{#2}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% executed just after preamble build is completed
							 | 
						
						
						
							| 
								
							 | 
							
								% warn about zero cols, and if prevtype type = u, put in end tabskip glue
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%
							 | 
						
						
						
							| 
								
							 | 
							
								{At least one column type must be declared for each IEEEeqnarray.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%num cols less than 1
							 | 
						
						
						
							| 
								
							 | 
							
								%if last type undefined, set default end tabskip glue
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Identify and return the column specifier's type code
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgetcoltype#1#2#3{%
							 | 
						
						
						
							| 
								
							 | 
							
								% use only the very first token to determine the type
							 | 
						
						
						
							| 
								
							 | 
							
								% \noindent is used as a delimiter as \end can be present here
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEgrabfirstoken#1\relax\relax\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								% \@IEEEgrabfirstoken has the first token, the rest are discarded
							 | 
						
						
						
							| 
								
							 | 
							
								% n = number
							 | 
						
						
						
							| 
								
							 | 
							
								% g = glue (any other char in catagory 12)
							 | 
						
						
						
							| 
								
							 | 
							
								% c = letter
							 | 
						
						
						
							| 
								
							 | 
							
								% e = \end
							 | 
						
						
						
							| 
								
							 | 
							
								% u = undefined
							 | 
						
						
						
							| 
								
							 | 
							
								% third argument: 0 = no error message, 1 = error on invalid char
							 | 
						
						
						
							| 
								
							 | 
							
								\let#2=u\relax% assume invalid until know otherwise
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgrabbedfirstoken\end\let#2=e\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences
							 | 
						
						
						
							| 
								
							 | 
							
								\if0\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if1\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if2\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if3\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if4\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if5\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if6\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if7\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if8\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if9\@IEEEgrabbedfirstoken\let#2=n\else
							 | 
						
						
						
							| 
								
							 | 
							
								\ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\else\ifcat a\@IEEEgrabbedfirstoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\if#2u\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%
							 | 
						
						
						
							| 
								
							 | 
							
								{Only letters, numerals and certain other symbols are allowed \MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								as IEEEeqnarray column specifiers.}\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% identify the current letter referenced column
							 | 
						
						
						
							| 
								
							 | 
							
								% if invalid, use a default column
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBPcurcolname{#1}\else% invalid column name
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								Using a default centering column instead}%
							 | 
						
						
						
							| 
								
							 | 
							
								{You must define IEEEeqnarray column types before use.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBPcurcolname{@IEEEdefault}\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% identify and return the predefined (punctuation) glue value
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgetcurglue#1#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								% ! = \! (neg small)  -0.16667em (-3/18 em)
							 | 
						
						
						
							| 
								
							 | 
							
								% , = \, (small)       0.16667em ( 3/18 em)
							 | 
						
						
						
							| 
								
							 | 
							
								% : = \: (med)         0.22222em ( 4/18 em)
							 | 
						
						
						
							| 
								
							 | 
							
								% ; = \; (large)       0.27778em ( 5/18 em)
							 | 
						
						
						
							| 
								
							 | 
							
								% ' = \quad            1em
							 | 
						
						
						
							| 
								
							 | 
							
								% " = \qquad           2em
							 | 
						
						
						
							| 
								
							 | 
							
								% . = 0.5\arraycolsep
							 | 
						
						
						
							| 
								
							 | 
							
								% / = \arraycolsep
							 | 
						
						
						
							| 
								
							 | 
							
								% ? = 2\arraycolsep
							 | 
						
						
						
							| 
								
							 | 
							
								% * = 1fil
							 | 
						
						
						
							| 
								
							 | 
							
								% + = \@IEEEeqnarraycolSEPcenter
							 | 
						
						
						
							| 
								
							 | 
							
								% - = \@IEEEeqnarraycolSEPzero
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that all em values are referenced to the math font (textfont2) fontdimen6
							 | 
						
						
						
							| 
								
							 | 
							
								% value for 1em.
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% use only the very first token to determine the type
							 | 
						
						
						
							| 
								
							 | 
							
								% this prevents errant tokens from getting in the main text
							 | 
						
						
						
							| 
								
							 | 
							
								% \noindent is used as a delimiter here
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEgrabfirstoken#1\relax\relax\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								% get the math font 1em value
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs
							 | 
						
						
						
							| 
								
							 | 
							
								% to gain access to the math (\textfont2) font's spacing parameters.
							 | 
						
						
						
							| 
								
							 | 
							
								% So we create a bogus box here that uses the math font to ensure
							 | 
						
						
						
							| 
								
							 | 
							
								% that \textfont2 is loaded and ready. If this is not done,
							 | 
						
						
						
							| 
								
							 | 
							
								% the \textfont2 stuff here may not work.
							 | 
						
						
						
							| 
								
							 | 
							
								% Thanks to Bernd Raichle for his 1997 post on this topic.
							 | 
						
						
						
							| 
								
							 | 
							
								{\setbox0=\hbox{$\displaystyle\relax$}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% fontdimen6 has the width of 1em (a quad).
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% identify the glue value based on the first token
							 | 
						
						
						
							| 
								
							 | 
							
								% we discard anything after the first
							 | 
						
						
						
							| 
								
							 | 
							
								\if!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if'\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if-\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPzero}\else
							 | 
						
						
						
							| 
								
							 | 
							
								\edef#2{\@IEEEeqnarraycolSEPzero}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								column specifications. Using a default value of\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								0pt instead}%
							 | 
						
						
						
							| 
								
							 | 
							
								{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak 
							 | 
						
						
						
							| 
								
							 | 
							
								IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process a numerical digit from the column specification
							 | 
						
						
						
							| 
								
							 | 
							
								% and look up the corresponding user defined glue value
							 | 
						
						
						
							| 
								
							 | 
							
								% can transform current type from n to g or a as the user defined glue is acquired
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								specifications. Ignoring consecutive glue specifiers\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								after the first}%
							 | 
						
						
						
							| 
								
							 | 
							
								{You cannot have two or more glue types next to each other\MessageBreak 
							 | 
						
						
						
							| 
								
							 | 
							
								in the IEEEeqnarray column specifications.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEBPcurnum=0\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% if we previously aborted a glue
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion
							 | 
						
						
						
							| 
								
							 | 
							
								\else%acquire this number
							 | 
						
						
						
							| 
								
							 | 
							
								% save the previous type before the numerical digits started
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\multiply\@IEEEBPcurnum by 10\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPnexttype n\else%close acquisition
							 | 
						
						
						
							| 
								
							 | 
							
								\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%user glue not defined
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								column specifications. Using a default value of\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								0pt instead}%
							 | 
						
						
						
							| 
								
							 | 
							
								{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% glue defined or not
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEBPcurnum=0\relax%ready for next acquisition
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%close acquisition, get glue
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%discard or acquire number
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%prevtype glue or not
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process an acquired glue
							 | 
						
						
						
							| 
								
							 | 
							
								% add any acquired column/glue pair to the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								% if this is the start glue, save it, but do nothing else 
							 | 
						
						
						
							| 
								
							 | 
							
								% as this is not used in the preamble, but before
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%not the start glue
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype g%ignore if back to back glues
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								specifications. Ignoring consecutive glue specifiers\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								after the first}%
							 | 
						
						
						
							| 
								
							 | 
							
								{You cannot have two or more glue types next to each other\MessageBreak 
							 | 
						
						
						
							| 
								
							 | 
							
								in the IEEEeqnarray column specifications.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurtype=a% abort this glue
							 | 
						
						
						
							| 
								
							 | 
							
								\else% not a back to back glue
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\toks0={##}%
							 | 
						
						
						
							| 
								
							 | 
							
								% make preamble advance col counter if this environment needs this
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% insert the column defintion into the preamble, being careful not to expand
							 | 
						
						
						
							| 
								
							 | 
							
								% the column definition
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\@IEEEBPcurcolname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\the\toks0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\@IEEEBPcurcolname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\endgroup}%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\else% error: non-start glue with no pending column
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								type in the column specifications. Ignoring this glue\MessageBreak 
							 | 
						
						
						
							| 
								
							 | 
							
								specifier}%
							 | 
						
						
						
							| 
								
							 | 
							
								{Except for the first and last positions, glue can be placed only\MessageBreak
							 | 
						
						
						
							| 
								
							 | 
							
								between column types.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBPcurtype=a% abort this glue
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% previous was a column
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% back-to-back glues
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% is start column glue
							 | 
						
						
						
							| 
								
							 | 
							
								\fi% prev type not a
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% process an acquired letter referenced column and, if necessary, add it to the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPnexttype n\else
							 | 
						
						
						
							| 
								
							 | 
							
								% we have a column followed by something other than a glue (or numeral glue)
							 | 
						
						
						
							| 
								
							 | 
							
								% so we must add this column to the preamble now
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first
							 | 
						
						
						
							| 
								
							 | 
							
								\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue
							 | 
						
						
						
							| 
								
							 | 
							
								\toks0={##}%
							 | 
						
						
						
							| 
								
							 | 
							
								% make preamble advance col counter if this environment needs this
							 | 
						
						
						
							| 
								
							 | 
							
								\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% insert the column definition into the preamble, being careful not to expand
							 | 
						
						
						
							| 
								
							 | 
							
								% the column definition
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\@IEEEBPcurcolname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\endcsname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\the\toks0}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendtoksA{\@IEEEBPcurcolname}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\relax\relax\relax\relax\relax\endgroup}%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%next type not numeral
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%next type not glue
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								%% END OF IEEEeqnarry DEFINITIONS
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% set up the running headings, this complex because of all the different
							 | 
						
						
						
							| 
								
							 | 
							
								% modes IEEEtran supports
							 | 
						
						
						
							| 
								
							 | 
							
								\if@twoside
							 | 
						
						
						
							| 
								
							 | 
							
								 \ifCLASSOPTIONtechnote
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\ps@headings{%
							 | 
						
						
						
							| 
								
							 | 
							
								       \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
							 | 
						
						
						
							| 
								
							 | 
							
								       \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
							 | 
						
						
						
							| 
								
							 | 
							
								       \ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								            \ifCLASSOPTIONdraftclsnofoot
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@oddfoot{}\def\@evenfoot{}%
							 | 
						
						
						
							| 
								
							 | 
							
								            \else
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
							 | 
						
						
						
							| 
								
							 | 
							
								            \fi
							 | 
						
						
						
							| 
								
							 | 
							
								       \else
							 | 
						
						
						
							| 
								
							 | 
							
								            \def\@oddfoot{}\def\@evenfoot{}
							 | 
						
						
						
							| 
								
							 | 
							
								       \fi}
							 | 
						
						
						
							| 
								
							 | 
							
								 \else % not a technote
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\ps@headings{%
							 | 
						
						
						
							| 
								
							 | 
							
								       \ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@oddhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@evenhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								       \else
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
							 | 
						
						
						
							| 
								
							 | 
							
								       \fi
							 | 
						
						
						
							| 
								
							 | 
							
								       \ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								            \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}
							 | 
						
						
						
							| 
								
							 | 
							
								            \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}
							 | 
						
						
						
							| 
								
							 | 
							
								            \ifCLASSOPTIONdraftclsnofoot
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@oddfoot{}\def\@evenfoot{}%
							 | 
						
						
						
							| 
								
							 | 
							
								            \else
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@oddfoot{\scriptsize\@date\hfil DRAFT}
							 | 
						
						
						
							| 
								
							 | 
							
								               \def\@evenfoot{\scriptsize DRAFT\hfil\@date}
							 | 
						
						
						
							| 
								
							 | 
							
								            \fi
							 | 
						
						
						
							| 
								
							 | 
							
								       \else
							 | 
						
						
						
							| 
								
							 | 
							
								            \def\@oddfoot{}\def\@evenfoot{}%
							 | 
						
						
						
							| 
								
							 | 
							
								       \fi}
							 | 
						
						
						
							| 
								
							 | 
							
								 \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\else % single side
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ps@headings{%
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@oddhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@evenhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@evenhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								          \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}
							 | 
						
						
						
							| 
								
							 | 
							
								          \def\@evenhead{}
							 | 
						
						
						
							| 
								
							 | 
							
								          \ifCLASSOPTIONdraftclsnofoot
							 | 
						
						
						
							| 
								
							 | 
							
								             \def\@oddfoot{}
							 | 
						
						
						
							| 
								
							 | 
							
								          \else
							 | 
						
						
						
							| 
								
							 | 
							
								             \def\@oddfoot{\scriptsize \@date \hfil DRAFT}
							 | 
						
						
						
							| 
								
							 | 
							
								          \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								         \def\@oddfoot{}
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\@evenfoot{}}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% title page style
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ps@IEEEtitlepagestyle{\def\@oddfoot{}\def\@evenfoot{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@oddhead{}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@evenhead{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONdraftclsnofoot\else
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								   % all non-draft mode footers
							 | 
						
						
						
							| 
								
							 | 
							
								   \if@IEEEusingpubid
							 | 
						
						
						
							| 
								
							 | 
							
								      % for title pages that are using a pubid
							 | 
						
						
						
							| 
								
							 | 
							
								      % do not repeat pubid if using peer review option
							 | 
						
						
						
							| 
								
							 | 
							
								      \ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								      \else
							 | 
						
						
						
							| 
								
							 | 
							
								         \footskip 0pt%
							 | 
						
						
						
							| 
								
							 | 
							
								         \ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								           \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								           \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								         \else
							 | 
						
						
						
							| 
								
							 | 
							
								           \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								           \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								         \fi
							 | 
						
						
						
							| 
								
							 | 
							
								      \fi
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% peer review cover page style
							 | 
						
						
						
							| 
								
							 | 
							
								\def\ps@IEEEpeerreviewcoverpagestyle{%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@oddhead{}\def\@evenhead{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@oddfoot{}\def\@evenfoot{}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONdraftclsnofoot\else
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								   % non-draft mode footers
							 | 
						
						
						
							| 
								
							 | 
							
								   \if@IEEEusingpubid
							 | 
						
						
						
							| 
								
							 | 
							
								      \footskip 0pt%
							 | 
						
						
						
							| 
								
							 | 
							
								      \ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \else
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								        \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \fi
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% start with empty headings
							 | 
						
						
						
							| 
								
							 | 
							
								\def\rightmark{}\def\leftmark{}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% Defines the command for putting the header. \footernote{TEXT} is the same
							 | 
						
						
						
							| 
								
							 | 
							
								%% as \markboth{TEXT}{TEXT}. 
							 | 
						
						
						
							| 
								
							 | 
							
								%% Note that all the text is forced into uppercase, if you have some text
							 | 
						
						
						
							| 
								
							 | 
							
								%% that needs to be in lower case, for instance et. al., then either manually
							 | 
						
						
						
							| 
								
							 | 
							
								%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the
							 | 
						
						
						
							| 
								
							 | 
							
								%% arguments to \markboth.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\markboth#1#2{\def\leftmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\rightmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{#2}}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\footernote#1{\markboth{#1}{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\today{\ifcase\month\or
							 | 
						
						
						
							| 
								
							 | 
							
								    January\or February\or March\or April\or May\or June\or
							 | 
						
						
						
							| 
								
							 | 
							
								    July\or August\or September\or October\or November\or December\fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \space\number\day, \number\year}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% CITATION AND BIBLIOGRAPHY COMMANDS
							 | 
						
						
						
							| 
								
							 | 
							
								%% 
							 | 
						
						
						
							| 
								
							 | 
							
								%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% Modify Latex2e \@citex to separate citations with "], ["
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@citex[#1]#2{%
							 | 
						
						
						
							| 
								
							 | 
							
								  \let\@citea\@empty
							 | 
						
						
						
							| 
								
							 | 
							
								  \@cite{\@for\@citeb:=#2\do
							 | 
						
						
						
							| 
								
							 | 
							
								    {\@citea\def\@citea{], [}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								     \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%
							 | 
						
						
						
							| 
								
							 | 
							
								       \G@refundefinedtrue
							 | 
						
						
						
							| 
								
							 | 
							
								       \@latex@warning
							 | 
						
						
						
							| 
								
							 | 
							
								         {Citation `\@citeb' on page \thepage \space undefined}}%
							 | 
						
						
						
							| 
								
							 | 
							
								       {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 we create hooks for the optional use of Donald Arseneau's
							 | 
						
						
						
							| 
								
							 | 
							
								% cite.sty package. cite.sty is "smart" and will notice that the
							 | 
						
						
						
							| 
								
							 | 
							
								% following format controls are already defined and will not
							 | 
						
						
						
							| 
								
							 | 
							
								% redefine them. The result will be the proper sorting of the
							 | 
						
						
						
							| 
								
							 | 
							
								% citation numbers and auto detection of 3 or more entry "ranges" -
							 | 
						
						
						
							| 
								
							 | 
							
								% all in IEEE style:  [1], [2], [5]--[7], [12]
							 | 
						
						
						
							| 
								
							 | 
							
								% This also allows for an optional note, i.e., \cite[mynote]{..}.
							 | 
						
						
						
							| 
								
							 | 
							
								% If the \cite with note has more than one reference, the note will
							 | 
						
						
						
							| 
								
							 | 
							
								% be applied to the last of the listed references. It is generally
							 | 
						
						
						
							| 
								
							 | 
							
								% desired that if a note is given, only one reference is listed in
							 | 
						
						
						
							| 
								
							 | 
							
								% that \cite.
							 | 
						
						
						
							| 
								
							 | 
							
								% Thanks to Mr. Arseneau for providing the required format arguments
							 | 
						
						
						
							| 
								
							 | 
							
								% to produce the IEEE style.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\citepunct{], [}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\citedash{]--[}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 default to using same font for urls made by url.sty
							 | 
						
						
						
							| 
								
							 | 
							
								\AtBeginDocument{\csname url@samestyle\endcsname}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 class files should always provide these
							 | 
						
						
						
							| 
								
							 | 
							
								\def\newblock{\hskip .11em\@plus.33em\@minus.07em}
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@openbib@code\@empty
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Provide support for the control entries of IEEEtran.bst V1.00 and later.
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 optional argument allows for a different aux file to be specified in
							 | 
						
						
						
							| 
								
							 | 
							
								% order to handle multiple bibliographies. For example, with multibib.sty:
							 | 
						
						
						
							| 
								
							 | 
							
								% \newcites{sec}{Secondary Literature}
							 | 
						
						
						
							| 
								
							 | 
							
								% \bstctlcite[@auxoutsec]{BSTcontrolhak}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@bstctlcite[#1]#2{\@bsphack
							 | 
						
						
						
							| 
								
							 | 
							
								  \@for\@citeb:=#2\do{%
							 | 
						
						
						
							| 
								
							 | 
							
								    \edef\@citeb{\expandafter\@firstofone\@citeb}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \@esphack}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 provide a way for a user to execute a command just before 
							 | 
						
						
						
							| 
								
							 | 
							
								% a given reference number - used to insert a \newpage to balance
							 | 
						
						
						
							| 
								
							 | 
							
								% the columns on the last page
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEtriggerrefnum{0}   % the default of zero means that
							 | 
						
						
						
							| 
								
							 | 
							
								                              % the command is not executed
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtriggercmd{\newpage}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% allow the user to alter the triggered command
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% allow user a way to specify the reference number just before the
							 | 
						
						
						
							| 
								
							 | 
							
								% command is executed
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% trigger command at the given reference
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpcountA by -1\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@biblabel#1{[#1]}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc journals left align the reference numbers
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocnotconfonly{\def\@biblabel#1{[#1]\hfill}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% controls bib item spacing
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEbibitemsep{0pt plus .5pt}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocconfonly{\def\IEEEbibitemsep{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thebibliography#1{\section*{\refname}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \addcontentsline{toc}{section}{\refname}%
							 | 
						
						
						
							| 
								
							 | 
							
								    % V1.6 add some rubber space here and provide a command trigger
							 | 
						
						
						
							| 
								
							 | 
							
								    \footnotesize\@IEEEcompsocconfonly{\small}\vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    \list{\@biblabel{\@arabic\c@enumiv}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    {\settowidth\labelwidth{\@biblabel{#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \leftmargin\labelwidth
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\leftmargin\labelsep\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \itemsep \IEEEbibitemsep\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \usecounter{enumiv}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\p@enumiv\@empty
							 | 
						
						
						
							| 
								
							 | 
							
								    \renewcommand\theenumiv{\@arabic\c@enumiv}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\@IEEElatexbibitem\bibitem%
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\newblock{\hskip .11em plus .33em minus .07em}%
							 | 
						
						
						
							| 
								
							 | 
							
								% originally:
							 | 
						
						
						
							| 
								
							 | 
							
								%   \sloppy\clubpenalty4000\widowpenalty4000%
							 | 
						
						
						
							| 
								
							 | 
							
								% by adding the \interlinepenalty here, we make it more
							 | 
						
						
						
							| 
								
							 | 
							
								% difficult, but not impossible, for LaTeX to break within a reference.
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE almost never breaks a reference (but they do it more often with
							 | 
						
						
						
							| 
								
							 | 
							
								% technotes). You may get an underfull vbox warning around the bibliography, 
							 | 
						
						
						
							| 
								
							 | 
							
								% but the final result will be much more like what IEEE will publish. 
							 | 
						
						
						
							| 
								
							 | 
							
								% MDS 11/2000
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%
							 | 
						
						
						
							| 
								
							 | 
							
								\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \sfcode`\.=1000\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endthebibliography=\endlist
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% TITLE PAGE COMMANDS
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEmembership is used to produce the sublargesize italic font used to indicate author 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE membership. compsoc uses a large size sans slant font
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEmembership#1{{\@IEEEnotcompsoconly{\sublargesize}\normalfont\@IEEEcompsoconly{\sffamily}\textit{#1}}}
							 | 
						
						
						
							| 
								
							 | 
							
								 
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEauthorrefmark{} produces a footnote type symbol to indicate author affiliation.
							 | 
						
						
						
							| 
								
							 | 
							
								% When given an argument of 1 to 9, \IEEEauthorrefmark{} follows the standard LaTeX footnote
							 | 
						
						
						
							| 
								
							 | 
							
								% symbol sequence convention. However, for arguments 10 and above, \IEEEauthorrefmark{} 
							 | 
						
						
						
							| 
								
							 | 
							
								% reverts to using lower case roman numerals, so it cannot overflow. Do note that you 
							 | 
						
						
						
							| 
								
							 | 
							
								% cannot use \footnotemark[] in place of \IEEEauthorrefmark{} within \author as the footnote
							 | 
						
						
						
							| 
								
							 | 
							
								% symbols will have been turned off to prevent \thanks from creating footnote marks.
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEauthorrefmark{} produces a symbol that appears to LaTeX as having zero vertical
							 | 
						
						
						
							| 
								
							 | 
							
								% height - this allows for a more compact line packing, but the user must ensure that
							 | 
						
						
						
							| 
								
							 | 
							
								% the interline spacing is large enough to prevent \IEEEauthorrefmark{} from colliding
							 | 
						
						
						
							| 
								
							 | 
							
								% with the text above.
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 make this a robust command
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%
							 | 
						
						
						
							| 
								
							 | 
							
								    \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%
							 | 
						
						
						
							| 
								
							 | 
							
								    \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% The default font styles for the author name and affiliation blocks (confmode)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockNstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize\@IEEEcompsocconfonly{\large}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockAstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\@IEEEcompsocconfonly{\itshape}\normalsize\@IEEEcompsocconfonly{\large}}
							 | 
						
						
						
							| 
								
							 | 
							
								% The default if the user does not use an author block
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthordefaulttextstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% spacing from title (or special paper notice) to author name blocks (confmode)
							 | 
						
						
						
							| 
								
							 | 
							
								% can be negative
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockconfadjspace{-0.25em}
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc conferences need more space here
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocconfonly{\def\@IEEEauthorblockconfadjspace{0.75\@IEEEnormalsizeunitybaselineskip}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% spacing between name and affiliation blocks (confmode)
							 | 
						
						
						
							| 
								
							 | 
							
								% This can be negative.
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE doesn't want any added spacing here, but I will leave these
							 | 
						
						
						
							| 
								
							 | 
							
								% controls in place in case they ever change their mind.
							 | 
						
						
						
							| 
								
							 | 
							
								% Personally, I like 0.75ex.
							 | 
						
						
						
							| 
								
							 | 
							
								%\def\@IEEEauthorblockNtopspace{0.75ex}
							 | 
						
						
						
							| 
								
							 | 
							
								%\def\@IEEEauthorblockAtopspace{0.75ex}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockNtopspace{0.0ex}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockAtopspace{0.0ex}
							 | 
						
						
						
							| 
								
							 | 
							
								% baseline spacing within name and affiliation blocks (confmode)
							 | 
						
						
						
							| 
								
							 | 
							
								% must be positive, spacings below certain values will make 
							 | 
						
						
						
							| 
								
							 | 
							
								% the position of line of text sensitive to the contents of the
							 | 
						
						
						
							| 
								
							 | 
							
								% line above it i.e., whether or not the prior line has descenders, 
							 | 
						
						
						
							| 
								
							 | 
							
								% subscripts, etc. For this reason it is a good idea to keep
							 | 
						
						
						
							| 
								
							 | 
							
								% these above 2.6ex
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockNinterlinespace{2.6ex}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockAinterlinespace{2.75ex}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This tracks the required strut size.
							 | 
						
						
						
							| 
								
							 | 
							
								% See the \@IEEEauthorhalign command for the actual default value used.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockXinterlinespace{2.7ex}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% variables to retain font size and style across groups
							 | 
						
						
						
							| 
								
							 | 
							
								% values given here have no effect as they will be overwritten later
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontsize{10}
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontbaselineskip{12}
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontencoding{OT1}
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontfamily{ptm}
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontseries{m}
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEESAVESTATEfontshape{n}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% saves the current font attributes
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\let\@IEEESAVESTATEfontencoding\f@encoding%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\let\@IEEESAVESTATEfontfamily\f@family%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\let\@IEEESAVESTATEfontseries\f@series%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\let\@IEEESAVESTATEfontshape\f@shape}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% restores the saved font attributes
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontencoding{\@IEEESAVESTATEfontencoding}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontfamily{\@IEEESAVESTATEfontfamily}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontseries{\@IEEESAVESTATEfontseries}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fontshape{\@IEEESAVESTATEfontshape}%
							 | 
						
						
						
							| 
								
							 | 
							
								\selectfont}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% variable to indicate if the current block is the first block in the column
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEprevauthorblockincol   \@IEEEprevauthorblockincolfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace
							 | 
						
						
						
							| 
								
							 | 
							
								% we use this technique to have complete manual control over the spacing of the lines
							 | 
						
						
						
							| 
								
							 | 
							
								% within the halign environment.
							 | 
						
						
						
							| 
								
							 | 
							
								% We set the below baseline portion at 30%, the above
							 | 
						
						
						
							| 
								
							 | 
							
								% baseline portion at 70% of the total length.
							 | 
						
						
						
							| 
								
							 | 
							
								% Responds to changes in the document's \baselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%
							 | 
						
						
						
							| 
								
							 | 
							
								\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% blocks to hold the authors' names and affilations. 
							 | 
						
						
						
							| 
								
							 | 
							
								% Makes formatting easy for conferences
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% use real definitions in conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								% name block
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEauthorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row
							 | 
						
						
						
							| 
								
							 | 
							
								% the \expandafter hides the \cr in conditional tex, see the array.sty docs
							 | 
						
						
						
							| 
								
							 | 
							
								% for details, probably not needed here as the \cr is in a macro
							 | 
						
						
						
							| 
								
							 | 
							
								% do a spacer row if needed
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
							 | 
						
						
						
							| 
								
							 | 
							
								%restore the correct strut value
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%
							 | 
						
						
						
							| 
								
							 | 
							
								% input the author names
							 | 
						
						
						
							| 
								
							 | 
							
								#1%
							 | 
						
						
						
							| 
								
							 | 
							
								% end the row if the user did not already
							 | 
						
						
						
							| 
								
							 | 
							
								\crcr}
							 | 
						
						
						
							| 
								
							 | 
							
								% spacer row for names
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% affiliation block
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEauthorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row
							 | 
						
						
						
							| 
								
							 | 
							
								% the \expandafter hides the \cr in conditional tex, see the array.sty docs
							 | 
						
						
						
							| 
								
							 | 
							
								% for details, probably not needed here as the \cr is in a macro
							 | 
						
						
						
							| 
								
							 | 
							
								% do a spacer row if needed
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEprevauthorblockincoltrue% we now have a block in this column
							 | 
						
						
						
							| 
								
							 | 
							
								%restore the correct strut value
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%
							 | 
						
						
						
							| 
								
							 | 
							
								% input the author affiliations
							 | 
						
						
						
							| 
								
							 | 
							
								#1%
							 | 
						
						
						
							| 
								
							 | 
							
								% end the row if the user did not already
							 | 
						
						
						
							| 
								
							 | 
							
								\crcr}
							 | 
						
						
						
							| 
								
							 | 
							
								% spacer row for affiliations
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% allow papers to compile even if author blocks are used in modes other
							 | 
						
						
						
							| 
								
							 | 
							
								% than conference or peerreviewca. For such cases, we provide dummy blocks.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONpeerreviewca\else
							 | 
						
						
						
							| 
								
							 | 
							
								      % not conference or peerreviewca mode
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\IEEEauthorblockN#1{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\IEEEauthorblockA#1{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we provide our own halign so as not to have to depend on tabular
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskip=0pt\relax% disable line spacing
							 | 
						
						
						
							| 
								
							 | 
							
								   \lineskiplimit=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \baselineskip=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEcurfontSAVE% save the current font
							 | 
						
						
						
							| 
								
							 | 
							
								   \mathsurround\z@\relax% no extra spacing around math
							 | 
						
						
						
							| 
								
							 | 
							
								   \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one
							 | 
						
						
						
							| 
								
							 | 
							
								   \tabskip=0pt\relax% no column spacing
							 | 
						
						
						
							| 
								
							 | 
							
								   \everycr{}% ensure no problems here
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEprevauthorblockincolfalse% no author blocks yet
							 | 
						
						
						
							| 
								
							 | 
							
								   \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space
							 | 
						
						
						
							| 
								
							 | 
							
								   \vtop\bgroup%vtop box
							 | 
						
						
						
							| 
								
							 | 
							
								   \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% ensure last line, exit from halign, close vbox
							 | 
						
						
						
							| 
								
							 | 
							
								\def\end@IEEEauthorhalign{\crcr\egroup\egroup}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% handle bogus star form
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% test and setup the optional argument to \\[]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% end the line and do the optional spacer
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flag to prevent multiple \and warning messages
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNand
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNandtrue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% if in conference or peerreviewca modes, we support the use of \and as \author is a
							 | 
						
						
						
							| 
								
							 | 
							
								% tabular environment, otherwise we warn the user that \and is invalid
							 | 
						
						
						
							| 
								
							 | 
							
								% outside of conference or peerreviewca modes.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\and{\relax} % provide a bogus \and that we will then override
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only
							 | 
						
						
						
							| 
								
							 | 
							
								                               when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference%
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONpeerreviewca
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% page clearing command
							 | 
						
						
						
							| 
								
							 | 
							
								% based on LaTeX2e's \cleardoublepage, but allows different page styles
							 | 
						
						
						
							| 
								
							 | 
							
								% for the inserted blank pages
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else
							 | 
						
						
						
							| 
								
							 | 
							
								\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% user command to invoke the title page
							 | 
						
						
						
							| 
								
							 | 
							
								\def\maketitle{\par%
							 | 
						
						
						
							| 
								
							 | 
							
								  \begingroup%
							 | 
						
						
						
							| 
								
							 | 
							
								  \normalfont%
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\thefootnote{}%  the \thanks{} mark type is empty
							 | 
						
						
						
							| 
								
							 | 
							
								  \def\footnotemark{}% and kill space from \thanks within author
							 | 
						
						
						
							| 
								
							 | 
							
								  \let\@makefnmark\relax% V1.7, must *really* kill footnotemark to remove all \textsuperscript spacing as well.
							 | 
						
						
						
							| 
								
							 | 
							
								  \footnotesize%       equal spacing between thanks lines
							 | 
						
						
						
							| 
								
							 | 
							
								  \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info
							 | 
						
						
						
							| 
								
							 | 
							
								  % V1.7 disable \thanks note indention for compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								  \@IEEEcompsoconly{\long\def\@makefntext##1{\parindent 1em\noindent\hbox{\@makefnmark}##1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \normalsize%
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								     \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
							 | 
						
						
						
							| 
								
							 | 
							
								     \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks%
							 | 
						
						
						
							| 
								
							 | 
							
								  \else
							 | 
						
						
						
							| 
								
							 | 
							
								     \if@twocolumn%
							 | 
						
						
						
							| 
								
							 | 
							
								        \ifCLASSOPTIONtechnote%
							 | 
						
						
						
							| 
								
							 | 
							
								           \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
							 | 
						
						
						
							| 
								
							 | 
							
								        \else
							 | 
						
						
						
							| 
								
							 | 
							
								           \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%
							 | 
						
						
						
							| 
								
							 | 
							
								        \fi
							 | 
						
						
						
							| 
								
							 | 
							
								     \else
							 | 
						
						
						
							| 
								
							 | 
							
								        \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%
							 | 
						
						
						
							| 
								
							 | 
							
								     \fi
							 | 
						
						
						
							| 
								
							 | 
							
								     \thispagestyle{IEEEtitlepagestyle}\@thanks%
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								  % pullup page for pubid if used.
							 | 
						
						
						
							| 
								
							 | 
							
								  \if@IEEEusingpubid
							 | 
						
						
						
							| 
								
							 | 
							
								     \enlargethispage{-\@IEEEpubidpullup}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi 
							 | 
						
						
						
							| 
								
							 | 
							
								  \endgroup
							 | 
						
						
						
							| 
								
							 | 
							
								  \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax
							 | 
						
						
						
							| 
								
							 | 
							
								  \gdef\@thanks{}%
							 | 
						
						
						
							| 
								
							 | 
							
								  % v1.6b do not clear these as we will need the title again for peer review papers
							 | 
						
						
						
							| 
								
							 | 
							
								  % \gdef\@author{}\gdef\@title{}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \let\thanks\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 parbox to format \@IEEEcompsoctitleabstractindextext
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEcompsoctitleabstractindextextbox#1{\parbox{0.915\textwidth}{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% formats the Title, authors names, affiliations and special paper notice
							 | 
						
						
						
							| 
								
							 | 
							
								% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional
							 | 
						
						
						
							| 
								
							 | 
							
								% spaces to enter the definition - use % at the end of each line
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@maketitle{\newpage
							 | 
						
						
						
							| 
								
							 | 
							
								\begin{center}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote% technotes
							 | 
						
						
						
							| 
								
							 | 
							
								   {\bfseries\large\@IEEEcompsoconly{\sffamily}\@title\par}\vskip 1.3em{\lineskip .5em\@IEEEcompsoconly{\sffamily}\@author
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEspecialpapernotice\par{\@IEEEcompsoconly{\vskip 1.5em\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par
							 | 
						
						
						
							| 
								
							 | 
							
								   \hfill\@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\else% not a technote
							 | 
						
						
						
							| 
								
							 | 
							
								   \vskip0.2em{\Huge\@IEEEcompsoconly{\sffamily}\@IEEEcompsocconfonly{\normalfont\normalsize\vskip 2\@IEEEnormalsizeunitybaselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								   \bfseries\Large}\@title\par}\vskip1.0em\par%
							 | 
						
						
						
							| 
								
							 | 
							
								   % V1.6 handle \author differently if in conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONconference%
							 | 
						
						
						
							| 
								
							 | 
							
								      {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
							 | 
						
						
						
							| 
								
							 | 
							
								       \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}\relax
							 | 
						
						
						
							| 
								
							 | 
							
								   \else% peerreviewca, peerreview or journal
							 | 
						
						
						
							| 
								
							 | 
							
								      \ifCLASSOPTIONpeerreviewca
							 | 
						
						
						
							| 
								
							 | 
							
								         % peerreviewca handles author names just like conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								         {\@IEEEcompsoconly{\sffamily}\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%
							 | 
						
						
						
							| 
								
							 | 
							
								          \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par
							 | 
						
						
						
							| 
								
							 | 
							
								          {\@IEEEcompsoconly{\vskip 1.5em\relax
							 | 
						
						
						
							| 
								
							 | 
							
								           \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill
							 | 
						
						
						
							| 
								
							 | 
							
								           \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
							 | 
						
						
						
							| 
								
							 | 
							
								      \else% journal or peerreview
							 | 
						
						
						
							| 
								
							 | 
							
								         {\lineskip.5em\@IEEEcompsoconly{\sffamily}\sublargesize\@author\@IEEEspecialpapernotice\par
							 | 
						
						
						
							| 
								
							 | 
							
								          {\@IEEEcompsoconly{\vskip 1.5em\relax
							 | 
						
						
						
							| 
								
							 | 
							
								           \@IEEEcompsoctitleabstractindextextbox{\@IEEEcompsoctitleabstractindextext}\par\hfill
							 | 
						
						
						
							| 
								
							 | 
							
								           \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax
							 | 
						
						
						
							| 
								
							 | 
							
								      \fi
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\end{center}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 Computer Society "diamond line" which follows index terms for nonconference papers
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEcompsocdiamondline{\vrule depth 0pt height 0.5pt width 4cm\hspace{7.5pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}%
							 | 
						
						
						
							| 
								
							 | 
							
								\hspace{7.5pt}\vrule depth 0pt height 0.5pt width 4cm\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 standard LateX2e \thanks, but with \itshape under compsoc. Also make it a \long\def
							 | 
						
						
						
							| 
								
							 | 
							
								% We also need to trigger the one-shot footnote rule
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtriggeroneshotfootnoterule{\global\@IEEEenableoneshotfootnoteruletrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\thanks#1{\footnotemark
							 | 
						
						
						
							| 
								
							 | 
							
								    \protected@xdef\@thanks{\@thanks
							 | 
						
						
						
							| 
								
							 | 
							
								        \protect\footnotetext[\the\c@footnote]{\@IEEEcompsoconly{\itshape
							 | 
						
						
						
							| 
								
							 | 
							
								        \protect\@IEEEtriggeroneshotfootnoterule\relax}\ignorespaces#1}}}
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@thanks\@empty
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 allow \author to contain \par's. This is needed to allow \thanks to contain \par.
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\author#1{\gdef\@author{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% in addition to setting up IEEEitemize, we need to remove a baselineskip space above and
							 | 
						
						
						
							| 
								
							 | 
							
								% below it because \list's \pars introduce blank lines because of the footnote struts.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsetupcompsocitemizelist{\def\labelitemi{$\bullet$}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\IEEElabelindent}{0pt}\setlength{\parskip}{0pt}%
							 | 
						
						
						
							| 
								
							 | 
							
								\setlength{\partopsep}{0pt}\setlength{\topsep}{0.5\baselineskip}\vspace{-1\baselineskip}\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flag for fake non-compsoc \IEEEcompsocthanksitem - prevents line break on very first item
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEbreakcompsocthanksitem \@IEEEbreakcompsocthanksitemfalse
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc bullet item \thanks
							 | 
						
						
						
							| 
								
							 | 
							
								% also, we need to redefine this to destroy the argument in \@IEEEdynamictitlevspace
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEcompsocitemizethanks#1{\relax\@IEEEbreakcompsocthanksitemfalse\footnotemark
							 | 
						
						
						
							| 
								
							 | 
							
								    \protected@xdef\@thanks{\@thanks
							 | 
						
						
						
							| 
								
							 | 
							
								        \protect\footnotetext[\the\c@footnote]{\itshape\protect\@IEEEtriggeroneshotfootnoterule
							 | 
						
						
						
							| 
								
							 | 
							
								        {\let\IEEEiedlistdecl\relax\protect\begin{IEEEitemize}[\protect\@IEEEsetupcompsocitemizelist]\ignorespaces#1\relax
							 | 
						
						
						
							| 
								
							 | 
							
								        \protect\end{IEEEitemize}}\protect\vspace{-1\baselineskip}}}}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareRobustCommand*{\IEEEcompsocthanksitem}{\item}
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								% non-compsoc, allow for dual compilation via rerouting to normal \thanks
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEcompsocitemizethanks#1{\thanks{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								% redirect to "pseudo-par" \hfil\break\indent after swallowing [] from \IEEEcompsocthanksitem[]
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareRobustCommand{\IEEEcompsocthanksitem}{\@ifnextchar [{\@IEEEthanksswallowoptionalarg}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\@IEEEthanksswallowoptionalarg[\relax]}}
							 | 
						
						
						
							| 
								
							 | 
							
								% be sure and break only after first item, be sure and ignore spaces after optional argument
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEthanksswallowoptionalarg[#1]{\relax\if@IEEEbreakcompsocthanksitem\hfil\break
							 | 
						
						
						
							| 
								
							 | 
							
								\indent\fi\@IEEEbreakcompsocthanksitemtrue\ignorespaces}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6b define the \IEEEpeerreviewmaketitle as needed
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtwocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								\twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace]
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\thispagestyle{IEEEtitlepagestyle}}
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpeerreviewmaketitle{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% peerreview formats the repeated title like the title in journal papers.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEpeerreviewmaketitle{\begin{center}\@IEEEcompsoconly{\sffamily}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par
							 | 
						
						
						
							| 
								
							 | 
							
								\end{center}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 
							 | 
						
						
						
							| 
								
							 | 
							
								% this is a static rubber spacer between the title/authors and the main text
							 | 
						
						
						
							| 
								
							 | 
							
								% used for single column text, or when the title appears in the first column
							 | 
						
						
						
							| 
								
							 | 
							
								% of two column text (technotes). 
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEstatictitlevskip{{\normalfont\normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								% adjust spacing to next text
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.6b handle peer review papers
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								% for peer review papers, the same value is used for both title pages
							 | 
						
						
						
							| 
								
							 | 
							
								% regardless of the other paper modes
							 | 
						
						
						
							| 
								
							 | 
							
								   \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONconference% conference
							 | 
						
						
						
							| 
								
							 | 
							
								      \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								   \else%
							 | 
						
						
						
							| 
								
							 | 
							
								      \ifCLASSOPTIONtechnote% technote
							 | 
						
						
						
							| 
								
							 | 
							
								         \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								      \else% journal uses more space
							 | 
						
						
						
							| 
								
							 | 
							
								         \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								      \fi
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6
							 | 
						
						
						
							| 
								
							 | 
							
								% This is a dynamically determined rigid spacer between the title/authors 
							 | 
						
						
						
							| 
								
							 | 
							
								% and the main text. This is used only for single column titles over two 
							 | 
						
						
						
							| 
								
							 | 
							
								% column text (most common)
							 | 
						
						
						
							| 
								
							 | 
							
								% This is bit tricky because we have to ensure that the textheight of the
							 | 
						
						
						
							| 
								
							 | 
							
								% main text is an integer multiple of \baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% otherwise underfull vbox problems may develop in the second column of the
							 | 
						
						
						
							| 
								
							 | 
							
								% text on the titlepage
							 | 
						
						
						
							| 
								
							 | 
							
								% The possible use of \IEEEpubid must also be taken into account.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEdynamictitlevspace{{%
							 | 
						
						
						
							| 
								
							 | 
							
								    % we run within a group so that all the macros can be forgotten when we are done
							 | 
						
						
						
							| 
								
							 | 
							
								    \long\def\thanks##1{\relax}%don't allow \thanks to run when we evaluate the vbox height
							 | 
						
						
						
							| 
								
							 | 
							
								    \long\def\IEEEcompsocitemizethanks##1{\relax}%don't allow \IEEEcompsocitemizethanks to run when we evaluate the vbox height
							 | 
						
						
						
							| 
								
							 | 
							
								    \normalfont\normalsize% we declare more descriptive variable names
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\@IEEEmaintextheight=\@IEEEtrantmpdimenA%height of the main text columns
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\@IEEEINTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines
							 | 
						
						
						
							| 
								
							 | 
							
								    % set the nominal and minimum values for the title spacer
							 | 
						
						
						
							| 
								
							 | 
							
								    % the dynamic algorithm will not allow the spacer size to
							 | 
						
						
						
							| 
								
							 | 
							
								    % become less than \@IEEEMINtitlevspace - instead it will be
							 | 
						
						
						
							| 
								
							 | 
							
								    % lengthened
							 | 
						
						
						
							| 
								
							 | 
							
								    % default to journal values
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\@IEEENORMtitlevspace{2.5\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\@IEEEMINtitlevspace{2\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								    % conferences and technotes need tighter spacing
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONconference%conference
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@IEEENORMtitlevspace{1\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@IEEEMINtitlevspace{0.75\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONtechnote%technote
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@IEEENORMtitlevspace{1\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								      \def\@IEEEMINtitlevspace{0.75\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    % get the height that the title will take up
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								       \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								       \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@maketitle}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEmaintextheight=-\@IEEEmaintextheight% title takes away from maintext, so reverse sign
							 | 
						
						
						
							| 
								
							 | 
							
								    % add the height of the page textheight
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEmaintextheight by \textheight%
							 | 
						
						
						
							| 
								
							 | 
							
								    % correct for title pages using pubid
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONpeerreview\else
							 | 
						
						
						
							| 
								
							 | 
							
								       % peerreview papers use the pubid on the cover page only.
							 | 
						
						
						
							| 
								
							 | 
							
								       % And the cover page uses a static spacer.
							 | 
						
						
						
							| 
								
							 | 
							
								       \if@IEEEusingpubid\advance\@IEEEmaintextheight by -\@IEEEpubidpullup\fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    % subtract off the nominal value of the title bottom spacer
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEmaintextheight by -\@IEEENORMtitlevspace%
							 | 
						
						
						
							| 
								
							 | 
							
								    % \topskip takes away some too
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEmaintextheight by -\topskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    % calculate the column height of the main text for lines
							 | 
						
						
						
							| 
								
							 | 
							
								    % now we calculate the main text height as if holding
							 | 
						
						
						
							| 
								
							 | 
							
								    % an integer number of \normalsize lines after the first
							 | 
						
						
						
							| 
								
							 | 
							
								    % and discard any excess fractional remainder
							 | 
						
						
						
							| 
								
							 | 
							
								    % we subtracted the first line, because the first line
							 | 
						
						
						
							| 
								
							 | 
							
								    % is placed \topskip into the maintext, not \baselineskip like the
							 | 
						
						
						
							| 
								
							 | 
							
								    % rest of the lines.
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEINTmaintextheight=\@IEEEmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								    \divide\@IEEEINTmaintextheight  by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    \multiply\@IEEEINTmaintextheight  by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    % now we calculate how much the title spacer height will
							 | 
						
						
						
							| 
								
							 | 
							
								    % have to be reduced from nominal (\@IEEEREDUCEmaintextheight is always
							 | 
						
						
						
							| 
								
							 | 
							
								    % a positive value) so that the maintext area will contain an integer
							 | 
						
						
						
							| 
								
							 | 
							
								    % number of normal size lines
							 | 
						
						
						
							| 
								
							 | 
							
								    % we change variable names here (to avoid confusion) as we no longer
							 | 
						
						
						
							| 
								
							 | 
							
								    % need \@IEEEINTmaintextheight and can reuse its dimen register
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\@IEEEREDUCEmaintextheight=\@IEEEINTmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEREDUCEmaintextheight by -\@IEEEmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEREDUCEmaintextheight by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    % this is the calculated height of the spacer
							 | 
						
						
						
							| 
								
							 | 
							
								    % we change variable names here (to avoid confusion) as we no longer
							 | 
						
						
						
							| 
								
							 | 
							
								    % need \@IEEEmaintextheight and can reuse its dimen register
							 | 
						
						
						
							| 
								
							 | 
							
								    \let\@IEEECOMPENSATElen=\@IEEEmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEECOMPENSATElen=\@IEEENORMtitlevspace% set the nominal value
							 | 
						
						
						
							| 
								
							 | 
							
								    % we go with the reduced length if it is smaller than an increase
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifdim\@IEEEREDUCEmaintextheight < 0.5\baselineskip\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								     \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								     % if the resulting spacer is too small back out and go with an increase instead
							 | 
						
						
						
							| 
								
							 | 
							
								     \ifdim\@IEEECOMPENSATElen<\@IEEEMINtitlevspace\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								      \advance\@IEEECOMPENSATElen by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								     \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \else%
							 | 
						
						
						
							| 
								
							 | 
							
								     % go with an increase because it is closer to the nominal than a decrease
							 | 
						
						
						
							| 
								
							 | 
							
								     \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%
							 | 
						
						
						
							| 
								
							 | 
							
								     \advance\@IEEECOMPENSATElen by \baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    % set the calculated rigid spacer
							 | 
						
						
						
							| 
								
							 | 
							
								    \vspace{\@IEEECOMPENSATElen}}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6
							 | 
						
						
						
							| 
								
							 | 
							
								% we allow the user access to the last part of the title area
							 | 
						
						
						
							| 
								
							 | 
							
								% useful in emergencies such as when a different spacing is needed
							 | 
						
						
						
							| 
								
							 | 
							
								% This text is NOT compensated for in the dynamic sizer.
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEaftertitletext=\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 provide a way for users to enter abstract and keywords
							 | 
						
						
						
							| 
								
							 | 
							
								% into the onecolumn title are. This text is compensated for
							 | 
						
						
						
							| 
								
							 | 
							
								% in the dynamic sizer.
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEcompsoctitleabstractindextext=\relax
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\IEEEcompsoctitleabstractindextext#1{\def\@IEEEcompsoctitleabstractindextext{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 provide a way for users to get the \@IEEEcompsoctitleabstractindextext if
							 | 
						
						
						
							| 
								
							 | 
							
								% not in compsoc journal mode - this way abstract and keywords can be placed
							 | 
						
						
						
							| 
								
							 | 
							
								% in their conventional position if not in compsoc mode.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEdisplaynotcompsoctitleabstractindextext{%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc% display if compsoc conf
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference\@IEEEcompsoctitleabstractindextext\fi
							 | 
						
						
						
							| 
								
							 | 
							
								\else% or if not compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsoctitleabstractindextext\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% command to allow alteration of baselinestretch, but only if the current
							 | 
						
						
						
							| 
								
							 | 
							
								% baselineskip is unity. Used to tweak the compsoc abstract and keywords line spacing.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtweakunitybaselinestretch#1{{\def\baselinestretch{1}\selectfont
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@tempskipa\baselineskip}\ifnum\@tempskipa=\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\baselinestretch{#1}\selectfont\fi\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% abstract and keywords are in \small, except 
							 | 
						
						
						
							| 
								
							 | 
							
								% for 9pt docs in which they are in \footnotesize
							 | 
						
						
						
							| 
								
							 | 
							
								% Because 9pt docs use an 8pt footnotesize, \small
							 | 
						
						
						
							| 
								
							 | 
							
								% becomes a rather awkward 8.5pt
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEabskeysecsize{\small}
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\CLASSOPTIONpt\@IEEEptsizenine
							 | 
						
						
						
							| 
								
							 | 
							
								 \def\@IEEEabskeysecsize{\footnotesize}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc journals use \footnotesize, compsoc conferences use normalsize
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsoconly{\def\@IEEEabskeysecsize{\footnotesize}}
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEcompsocconfonly{\def\@IEEEabskeysecsize{\normalsize}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 have abstract and keywords strip leading spaces, pars and newlines
							 | 
						
						
						
							| 
								
							 | 
							
								% so that spacing is more tightly controlled.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\abstract{\normalfont
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								      \@IEEEabskeysecsize\bfseries\textit{\abstractname}---\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in 
							 | 
						
						
						
							| 
								
							 | 
							
								% conference mode (the heading already has this much above it)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endabstract{\relax\ifCLASSOPTIONconference\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \normalfont\normalsize}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEkeywords{\normalfont
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								      \@IEEEabskeysecsize\bfseries\textit{\IEEEkeywordsname}---\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEkeywords{\relax\ifCLASSOPTIONtechnote\vspace{1.34ex}\else\vspace{0.67ex}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								    \par\if@twocolumn\else\endquotation\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \normalfont\normalsize}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc keywords index terms
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifCLASSOPTIONconference% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								\def\abstract{\normalfont
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\@IEEEabskeysecsize\textbf{\large\abstractname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								      \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%
							 | 
						
						
						
							| 
								
							 | 
							
								      \par\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEkeywords{\normalfont\vskip 1.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\@IEEEabskeysecsize\textbf{\large\IEEEkeywordsname}\end{center}\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								      \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%
							 | 
						
						
						
							| 
								
							 | 
							
								      \par\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								  \else% compsoc not conference
							 | 
						
						
						
							| 
								
							 | 
							
								\def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								      \@IEEEabskeysecsize\noindent\textbf{\abstractname}---\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\end{center}\quotation\@IEEEabskeysecsize%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily
							 | 
						
						
						
							| 
								
							 | 
							
								    \if@twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								      \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								      \textbf{\IEEEkeywordsname}---\relax
							 | 
						
						
						
							| 
								
							 | 
							
								    \else
							 | 
						
						
						
							| 
								
							 | 
							
								      \begin{center}\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\end{center}\quotation\@IEEEabskeysecsize%
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi\@IEEEgobbleleadPARNLSP}
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% gobbles all leading \, \\ and \par, upon finding first token that
							 | 
						
						
						
							| 
								
							 | 
							
								% is not a \ , \\ or a \par, it ceases and returns that token
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% used to strip leading \, \\ and \par from the input
							 | 
						
						
						
							| 
								
							 | 
							
								% so that such things in the beginning of an environment will not
							 | 
						
						
						
							| 
								
							 | 
							
								% affect the formatting of the text
							 | 
						
						
						
							| 
								
							 | 
							
								\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEgobbleleadPARNLSPtoken#1%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEgobbleleadPARtoken=\par%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEgobbleleadNLtoken=\\%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEgobbleleadSPtoken=\ %
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEgobbleleadSPMACRO{\ }%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEswallowthistoken=1%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEswallowthistoken=1%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEswallowthistoken=1%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% a control space will come in as a macro
							 | 
						
						
						
							| 
								
							 | 
							
								% when it is the last one on a line
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEswallowthistoken=1%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% if we have to swallow this token, do so and taste the next one
							 | 
						
						
						
							| 
								
							 | 
							
								% else spit it out and stop gobbling
							 | 
						
						
						
							| 
								
							 | 
							
								\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEnextgobbleleadPARNLSP=#1\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEnextgobbleleadPARNLSP}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% TITLING OF SECTIONS
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsectpunct{:\ \,}  % Punctuation after run-in section heading  (headings which are
							 | 
						
						
						
							| 
								
							 | 
							
								                            % part of the paragraphs), need little bit more than a single space
							 | 
						
						
						
							| 
								
							 | 
							
								                            % spacing from section number to title
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc conferences use regular period/space punctuation
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsectpunct{.\ }
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc journals need extra spacing
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference\else
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 1em\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%v1.7 put {} after #6 to allow for some types of user font control
							 | 
						
						
						
							| 
								
							 | 
							
								%and use \@@par rather than \par
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@sect#1#2#3#4#5#6[#7]#8{%
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifnum #2>\c@secnumdepth
							 | 
						
						
						
							| 
								
							 | 
							
								     \let\@svsec\@empty
							 | 
						
						
						
							| 
								
							 | 
							
								  \else
							 | 
						
						
						
							| 
								
							 | 
							
								     \refstepcounter{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								     % load section label and spacer into \@svsec
							 | 
						
						
						
							| 
								
							 | 
							
								     \protected@edef\@svsec{\@seccntformat{#1}\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								  \@tempskipa #5\relax
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high
							 | 
						
						
						
							| 
								
							 | 
							
								     \begingroup #6{\relax% or low level heading
							 | 
						
						
						
							| 
								
							 | 
							
								      \noindent % subsections are NOT indented
							 | 
						
						
						
							| 
								
							 | 
							
								       % print top level headings. \@svsec is label, #8 is heading title
							 | 
						
						
						
							| 
								
							 | 
							
								       % IEEE does not block indent the section title text, it flows like normal
							 | 
						
						
						
							| 
								
							 | 
							
								       {\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\@@par}}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \endgroup
							 | 
						
						
						
							| 
								
							 | 
							
								     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
							 | 
						
						
						
							| 
								
							 | 
							
								               \protect\numberline{\csname the#1\endcsname}\fi#7}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \else % printout low level headings
							 | 
						
						
						
							| 
								
							 | 
							
								     % svsechd seems to swallow the trailing space, protect it with \mbox{}
							 | 
						
						
						
							| 
								
							 | 
							
								     % got rid of sectionmark stuff
							 | 
						
						
						
							| 
								
							 | 
							
								     \def\@svsechd{#6{\hskip #3\relax\@svsec #8\@IEEEsectpunct\mbox{}}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else
							 | 
						
						
						
							| 
								
							 | 
							
								               \protect\numberline{\csname the#1\endcsname}\fi#7}}%
							 | 
						
						
						
							| 
								
							 | 
							
								  \fi%skip down
							 | 
						
						
						
							| 
								
							 | 
							
								  \@xsect{#5}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% section* handler
							 | 
						
						
						
							| 
								
							 | 
							
								%v1.7 put {} after #4 to allow for some types of user font control
							 | 
						
						
						
							| 
								
							 | 
							
								%and use \@@par rather than \par
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
							 | 
						
						
						
							| 
								
							 | 
							
								  \ifdim \@tempskipa>\z@
							 | 
						
						
						
							| 
								
							 | 
							
								     %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
							 | 
						
						
						
							| 
								
							 | 
							
								     % IEEE does not block indent the section title text, it flows like normal
							 | 
						
						
						
							| 
								
							 | 
							
								     \begingroup \noindent #4{\relax{\hskip #1}{\interlinepenalty \@M #5\@@par}}\endgroup
							 | 
						
						
						
							| 
								
							 | 
							
								  % svsechd swallows the trailing space, protect it with \mbox{}
							 | 
						
						
						
							| 
								
							 | 
							
								  \else \def\@svsechd{#4{\hskip #1\relax #5\@IEEEsectpunct\mbox{}}}\fi
							 | 
						
						
						
							| 
								
							 | 
							
								  \@xsect{#3}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% SECTION heading spacing and font
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								% arguments are: #1 - sectiontype name
							 | 
						
						
						
							| 
								
							 | 
							
								% (for \@sect)   #2 - section level
							 | 
						
						
						
							| 
								
							 | 
							
								%                #3 - section heading indent
							 | 
						
						
						
							| 
								
							 | 
							
								%                #4 - top separation (absolute value used, neg indicates not to indent main text)
							 | 
						
						
						
							| 
								
							 | 
							
								%                     If negative, make stretch parts negative too!
							 | 
						
						
						
							| 
								
							 | 
							
								%                #5 - (absolute value used) positive: bottom separation after heading,
							 | 
						
						
						
							| 
								
							 | 
							
								%                      negative: amount to indent main text after heading
							 | 
						
						
						
							| 
								
							 | 
							
								%                Both #4 and #5 negative means to indent main text and use negative top separation
							 | 
						
						
						
							| 
								
							 | 
							
								%                #6 - font control
							 | 
						
						
						
							| 
								
							 | 
							
								% You've got to have \normalfont\normalsize in the font specs below to prevent
							 | 
						
						
						
							| 
								
							 | 
							
								% trouble when you do something like:
							 | 
						
						
						
							| 
								
							 | 
							
								% \section{Note}{\ttfamily TT-TEXT} is known to ... 
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE sometimes REALLY stretches the area before a section
							 | 
						
						
						
							| 
								
							 | 
							
								% heading by up to about 0.5in. However, it may not be a good
							 | 
						
						
						
							| 
								
							 | 
							
								% idea to let LaTeX have quite this much rubber.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference%
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE wants section heading spacing to decrease for conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else % for journals
							 | 
						
						
						
							| 
								
							 | 
							
								\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% for both journals and conferences
							 | 
						
						
						
							| 
								
							 | 
							
								% decided to put in a little rubber above the section, might help somebody
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0ex}{\normalfont\normalsize\itshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0ex}{\normalfont\normalsize\itshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								% compsoc conference
							 | 
						
						
						
							| 
								
							 | 
							
								\def\section{\@startsection{section}{1}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\large\bfseries}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsection{\@startsection{subsection}{2}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\sublargesize\bfseries}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0ex}{\normalfont\normalsize\bfseries}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0ex}{\normalfont\normalsize}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else% compsoc journals
							 | 
						
						
						
							| 
								
							 | 
							
								% use negative top separation as compsoc journals do not indent paragraphs after section titles
							 | 
						
						
						
							| 
								
							 | 
							
								\def\section{\@startsection{section}{1}{\z@}{-3ex plus -2ex minus -1.5ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus 1ex minus 0ex}{\normalfont\large\sffamily\bfseries\scshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% Note that subsection and smaller may not be correct for the Computer Society,
							 | 
						
						
						
							| 
								
							 | 
							
								% I have to look up an example.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsection{\@startsection{subsection}{2}{\z@}{-3.5ex plus -1.5ex minus -1.5ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\sffamily\bfseries}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex plus -1ex minus -1ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0.5ex plus 0.5ex minus 0ex}{\normalfont\normalsize\sffamily\itshape}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{-0ex plus -0.1ex minus -0.1ex}%
							 | 
						
						
						
							| 
								
							 | 
							
								{0ex}{\normalfont\normalsize}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% ENVIRONMENTS
							 | 
						
						
						
							| 
								
							 | 
							
								% "box" symbols at end of proofs
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 some journals use an open box instead that will just fit around a closed one
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEQED{\IEEEQEDopen}   % default to open for compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\else
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEQED{\IEEEQEDclosed} % otherwise default to closed
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.7 name change to avoid namespace collision with amsthm. Also add support
							 | 
						
						
						
							| 
								
							 | 
							
								% for an optional argument.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEproof[#1]{\par\noindent\hspace{2em}{\itshape #1: }}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endIEEEproof{\hspace*{\fill}~\IEEEQED\par}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%\itemindent is set to \z@ by list, so define new temporary variable
							 | 
						
						
						
							| 
								
							 | 
							
								\newdimen\@IEEEtmpitemindent
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily\trivlist%
							 | 
						
						
						
							| 
								
							 | 
							
								    \item[\hskip \labelsep{\indent\itshape #1\ #2:}]\itemindent\@IEEEtmpitemindent}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\topsep 0pt\rmfamily \trivlist%
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 IEEE is back to using () around theorem names which are also in italics
							 | 
						
						
						
							| 
								
							 | 
							
								% Thanks to Christian Peel for reporting this.
							 | 
						
						
						
							| 
								
							 | 
							
								    \item[\hskip\labelsep{\indent\itshape #1\ #2\ (#3):}]\itemindent\@IEEEtmpitemindent}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 remove bogus \unskip that caused equations in theorems to collide with
							 | 
						
						
						
							| 
								
							 | 
							
								% lines below.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@endtheorem{\endtrivlist}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6
							 | 
						
						
						
							| 
								
							 | 
							
								% display command for the section the theorem is in - so that \thesection
							 | 
						
						
						
							| 
								
							 | 
							
								% is not used as this will be in Roman numerals when we want arabic.
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number
							 | 
						
						
						
							| 
								
							 | 
							
								% (second part) display and \def\@thmcountersep{.} as a separator.
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 intercept calls to the section counter and reroute to \@IEEEthmcounterinsection
							 | 
						
						
						
							| 
								
							 | 
							
								% to allow \appendix(ices} to override as needed.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% special handler for sections, allows appendix(ices) to override
							 | 
						
						
						
							| 
								
							 | 
							
								\gdef\@IEEEthmcounterinsection#1{\arabic{#1}}
							 | 
						
						
						
							| 
								
							 | 
							
								% string macro
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\@IEEEstringsection{section}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterinsection
							 | 
						
						
						
							| 
								
							 | 
							
								% if section in_counter is used
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@xnthm#1#2[#3]{%
							 | 
						
						
						
							| 
								
							 | 
							
								  \expandafter\@ifdefinable\csname #1\endcsname
							 | 
						
						
						
							| 
								
							 | 
							
								    {\@definecounter{#1}\@newctr{#1}[#3]%
							 | 
						
						
						
							| 
								
							 | 
							
								     \edef\@IEEEstringtmp{#3}
							 | 
						
						
						
							| 
								
							 | 
							
								     \ifx\@IEEEstringtmp\@IEEEstringsection
							 | 
						
						
						
							| 
								
							 | 
							
								     \expandafter\xdef\csname the#1\endcsname{%
							 | 
						
						
						
							| 
								
							 | 
							
								     \noexpand\@IEEEthmcounterinsection{#3}\@thmcountersep
							 | 
						
						
						
							| 
								
							 | 
							
								          \@thmcounter{#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \else
							 | 
						
						
						
							| 
								
							 | 
							
								     \expandafter\xdef\csname the#1\endcsname{%
							 | 
						
						
						
							| 
								
							 | 
							
								       \expandafter\noexpand\csname the#3\endcsname \@thmcountersep
							 | 
						
						
						
							| 
								
							 | 
							
								          \@thmcounter{#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \fi
							 | 
						
						
						
							| 
								
							 | 
							
								     \global\@namedef{#1}{\@thm{#1}{#2}}%
							 | 
						
						
						
							| 
								
							 | 
							
								     \global\@namedef{end#1}{\@endtheorem}}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% SET UP THE DEFAULT PAGESTYLE
							 | 
						
						
						
							| 
								
							 | 
							
								\ps@headings
							 | 
						
						
						
							| 
								
							 | 
							
								\pagenumbering{arabic}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% normally the page counter starts at 1
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{page}{1}
							 | 
						
						
						
							| 
								
							 | 
							
								% however, for peerreview the cover sheet is page 0 or page -1
							 | 
						
						
						
							| 
								
							 | 
							
								% (for duplex printing)
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONpeerreview
							 | 
						
						
						
							| 
								
							 | 
							
								   \if@twoside
							 | 
						
						
						
							| 
								
							 | 
							
								      \setcounter{page}{-1}
							 | 
						
						
						
							| 
								
							 | 
							
								   \else
							 | 
						
						
						
							| 
								
							 | 
							
								      \setcounter{page}{0}
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% standard book class behavior - let bottom line float up and down as
							 | 
						
						
						
							| 
								
							 | 
							
								% needed when single sided
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtwoside\else\raggedbottom\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% if two column - turn on twocolumn, allow word spacings to stretch more and
							 | 
						
						
						
							| 
								
							 | 
							
								% enforce a rigid position for the last lines
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtwocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								% the peer review option delays invoking twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								   \ifCLASSOPTIONpeerreview\else
							 | 
						
						
						
							| 
								
							 | 
							
								      \twocolumn
							 | 
						
						
						
							| 
								
							 | 
							
								   \fi
							 | 
						
						
						
							| 
								
							 | 
							
								\sloppy 
							 | 
						
						
						
							| 
								
							 | 
							
								\flushbottom
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \APPENDIX and \APPENDICES definitions
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% This is the \@ifmtarg command from the LaTeX ifmtarg package
							 | 
						
						
						
							| 
								
							 | 
							
								% by Peter Wilson (CUA) and Donald Arseneau
							 | 
						
						
						
							| 
								
							 | 
							
								% \@ifmtarg is used to determine if an argument to a command
							 | 
						
						
						
							| 
								
							 | 
							
								% is present or not.
							 | 
						
						
						
							| 
								
							 | 
							
								% For instance:
							 | 
						
						
						
							| 
								
							 | 
							
								% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}
							 | 
						
						
						
							| 
								
							 | 
							
								% \@ifmtarg is used with our redefined \section command if
							 | 
						
						
						
							| 
								
							 | 
							
								% \appendices is invoked.
							 | 
						
						
						
							| 
								
							 | 
							
								% The command \section will behave slightly differently depending
							 | 
						
						
						
							| 
								
							 | 
							
								% on whether the user specifies a title: 
							 | 
						
						
						
							| 
								
							 | 
							
								% \section{My appendix title}
							 | 
						
						
						
							| 
								
							 | 
							
								% or not:
							 | 
						
						
						
							| 
								
							 | 
							
								% \section{}
							 | 
						
						
						
							| 
								
							 | 
							
								% This way, we can eliminate the blank lines where the title
							 | 
						
						
						
							| 
								
							 | 
							
								% would be, and the unneeded : after Appendix in the table of
							 | 
						
						
						
							| 
								
							 | 
							
								% contents 
							 | 
						
						
						
							| 
								
							 | 
							
								\begingroup
							 | 
						
						
						
							| 
								
							 | 
							
								\catcode`\Q=3
							 | 
						
						
						
							| 
								
							 | 
							
								\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}
							 | 
						
						
						
							| 
								
							 | 
							
								\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}
							 | 
						
						
						
							| 
								
							 | 
							
								\endgroup
							 | 
						
						
						
							| 
								
							 | 
							
								% end of \@ifmtarg defs
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7
							 | 
						
						
						
							| 
								
							 | 
							
								% command that allows the one time saving of the original definition
							 | 
						
						
						
							| 
								
							 | 
							
								% of section to \@IEEEappendixsavesection for \appendix or \appendices 
							 | 
						
						
						
							| 
								
							 | 
							
								% we don't save \section here as it may be redefined later by other
							 | 
						
						
						
							| 
								
							 | 
							
								% packages (hyperref.sty, etc.)
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEsaveoriginalsectiononce{\let\@IEEEappendixsavesection\section
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEsaveoriginalsectiononce\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% neat trick to grab and process the argument from \section{argument}
							 | 
						
						
						
							| 
								
							 | 
							
								% we process differently if the user invoked \section{} with no
							 | 
						
						
						
							| 
								
							 | 
							
								% argument (title)
							 | 
						
						
						
							| 
								
							 | 
							
								% note we reroute the call to the old \section*
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEprocessthesectionargument#1{%
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifmtarg{#1}{%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendixsavesection*{\appendixname~\thesectiondis}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{section}{\appendixname~\thesection}}{%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEappendixsavesection*{\appendixname~\thesectiondis \\* #1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{section}{\appendixname~\thesection: #1}}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% we use this if the user calls \section{} after
							 | 
						
						
						
							| 
								
							 | 
							
								% \appendix-- which has no meaning. So, we ignore the
							 | 
						
						
						
							| 
								
							 | 
							
								% command and its argument. Then, warn the user.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless
							 | 
						
						
						
							| 
								
							 | 
							
								\protect\section\space in Appendix (line \the\inputlineno).}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% remember \thesection forms will be displayed in \ref calls
							 | 
						
						
						
							| 
								
							 | 
							
								% and in the Table of Contents.
							 | 
						
						
						
							| 
								
							 | 
							
								% The \sectiondis form is used in the actual heading itself
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% appendix command for one single appendix
							 | 
						
						
						
							| 
								
							 | 
							
								% normally has no heading. However, if you want a 
							 | 
						
						
						
							| 
								
							 | 
							
								% heading, you can do so via the optional argument:
							 | 
						
						
						
							| 
								
							 | 
							
								% \appendix[Optional Heading]
							 | 
						
						
						
							| 
								
							 | 
							
								\def\appendix{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\renewcommand{\appendix}[1][]{\@IEEEsaveoriginalsectiononce\par
							 | 
						
						
						
							| 
								
							 | 
							
								    % v1.6 keep hyperref's identifiers unique
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\theHsection{Appendix.A}%
							 | 
						
						
						
							| 
								
							 | 
							
								    % v1.6 adjust hyperref's string name for the section
							 | 
						
						
						
							| 
								
							 | 
							
								    \xdef\Hy@chapapp{appendix}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{section}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{subsection}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{subsubsection}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{paragraph}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesection{A}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesectiondis{}% 
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesubsection{\Alph{subsection}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\@IEEEthmcounterinsection##1{A}
							 | 
						
						
						
							| 
								
							 | 
							
								    \refstepcounter{section}% update the \ref counter
							 | 
						
						
						
							| 
								
							 | 
							
								    \@ifmtarg{#1}{\@IEEEappendixsavesection*{\appendixname}%
							 | 
						
						
						
							| 
								
							 | 
							
								                  \addcontentsline{toc}{section}{\appendixname}}{%
							 | 
						
						
						
							| 
								
							 | 
							
								             \@IEEEappendixsavesection*{\appendixname~\\* #1}%
							 | 
						
						
						
							| 
								
							 | 
							
								             \addcontentsline{toc}{section}{\appendixname: #1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    % redefine \section command for appendix
							 | 
						
						
						
							| 
								
							 | 
							
								    % leave \section* as is
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\section{\@ifstar{\@IEEEappendixsavesection*}{%
							 | 
						
						
						
							| 
								
							 | 
							
								                    \@IEEEdestroythesectionargument}}% throw out the argument
							 | 
						
						
						
							| 
								
							 | 
							
								                                                     % of the normal form
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% appendices command for multiple appendices
							 | 
						
						
						
							| 
								
							 | 
							
								% user then calls \section with an argument (possibly empty) to
							 | 
						
						
						
							| 
								
							 | 
							
								% declare the individual appendices
							 | 
						
						
						
							| 
								
							 | 
							
								\def\appendices{\@IEEEsaveoriginalsectiononce\par
							 | 
						
						
						
							| 
								
							 | 
							
								    % v1.6 keep hyperref's identifiers unique
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\theHsection{Appendix.\Alph{section}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    % v1.6 adjust hyperref's string name for the section
							 | 
						
						
						
							| 
								
							 | 
							
								    \xdef\Hy@chapapp{appendix}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{section}{-1}% we want \refstepcounter to use section 0
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{subsection}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{subsubsection}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{paragraph}{0}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \ifCLASSOPTIONromanappendices%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesection{\Roman{section}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesectiondis{\Roman{section}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEcompsocconfonly{\gdef\thesectiondis{\Roman{section}.}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\@IEEEthmcounterinsection##1{A\arabic{##1}}
							 | 
						
						
						
							| 
								
							 | 
							
								    \else%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesection{\Alph{section}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\thesectiondis{\Alph{section}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEcompsocconfonly{\gdef\thesectiondis{\Alph{section}.}}%
							 | 
						
						
						
							| 
								
							 | 
							
								    \gdef\@IEEEthmcounterinsection##1{\Alph{##1}}
							 | 
						
						
						
							| 
								
							 | 
							
								    \fi%
							 | 
						
						
						
							| 
								
							 | 
							
								    \refstepcounter{section}% update the \ref counter
							 | 
						
						
						
							| 
								
							 | 
							
								    \setcounter{section}{0}% NEXT \section will be the FIRST appendix
							 | 
						
						
						
							| 
								
							 | 
							
								    % redefine \section command for appendices
							 | 
						
						
						
							| 
								
							 | 
							
								    % leave \section* as is
							 | 
						
						
						
							| 
								
							 | 
							
								    \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form
							 | 
						
						
						
							| 
								
							 | 
							
								                    \refstepcounter{section}% or is a new section so,
							 | 
						
						
						
							| 
								
							 | 
							
								                    \@IEEEprocessthesectionargument}}% process the argument 
							 | 
						
						
						
							| 
								
							 | 
							
								                                                 % of the normal form
							 | 
						
						
						
							| 
								
							 | 
							
								}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								% Definition for the big two line drop cap letter at the beginning of the
							 | 
						
						
						
							| 
								
							 | 
							
								% first paragraph of journal papers. The first argument is the first letter
							 | 
						
						
						
							| 
								
							 | 
							
								% of the first word, the second argument is the remaining letters of the
							 | 
						
						
						
							| 
								
							 | 
							
								% first word which will be rendered in upper case.
							 | 
						
						
						
							| 
								
							 | 
							
								% In V1.6 this has been completely rewritten to:
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% 1. no longer have problems when the user begins an environment
							 | 
						
						
						
							| 
								
							 | 
							
								%    within the paragraph that uses \IEEEPARstart.
							 | 
						
						
						
							| 
								
							 | 
							
								% 2. auto-detect and use the current font family
							 | 
						
						
						
							| 
								
							 | 
							
								% 3. revise handling of the space at the end of the first word so that
							 | 
						
						
						
							| 
								
							 | 
							
								%    interword glue will now work as normal.
							 | 
						
						
						
							| 
								
							 | 
							
								% 4. produce correctly aligned edges for the (two) indented lines.
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% We generalize things via control macros - playing with these is fun too.
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 added more control macros to make it easy for IEEEtrantools.sty users
							 | 
						
						
						
							| 
								
							 | 
							
								% to change the font style.
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% the number of lines that are indented to clear it
							 | 
						
						
						
							| 
								
							 | 
							
								% may need to increase if using decenders
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartDROPLINES{2}
							 | 
						
						
						
							| 
								
							 | 
							
								% minimum number of lines left on a page to allow a \@IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								% Does not take into consideration rubber shrink, so it tends to
							 | 
						
						
						
							| 
								
							 | 
							
								% be overly cautious
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartMINPAGELINES{2}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 the height of the drop cap is adjusted to match the height of this text
							 | 
						
						
						
							| 
								
							 | 
							
								% in the current font (when \IEEEPARstart is called).
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartHEIGHTTEXT{T}
							 | 
						
						
						
							| 
								
							 | 
							
								% the depth the letter is lowered below the baseline
							 | 
						
						
						
							| 
								
							 | 
							
								% the height (and size) of the letter is determined by the sum
							 | 
						
						
						
							| 
								
							 | 
							
								% of this value and the height of the \@IEEEPARstartHEIGHTTEXT in the current
							 | 
						
						
						
							| 
								
							 | 
							
								% font. It is a good idea to set this value in terms of the baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% so that it can respond to changes therein.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartDROPDEPTH{1.1\baselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 the font the drop cap will be rendered in,
							 | 
						
						
						
							| 
								
							 | 
							
								% can take zero or one argument.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartFONTSTYLE{\bfseries}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 any additional, non-font related commands needed to modify
							 | 
						
						
						
							| 
								
							 | 
							
								% the drop cap letter, can take zero or one argument.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartCAPSTYLE{\MakeUppercase}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 the font that will be used to render the rest of the word,
							 | 
						
						
						
							| 
								
							 | 
							
								% can take zero or one argument.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartWORDFONTSTYLE{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 any additional, non-font related commands needed to modify
							 | 
						
						
						
							| 
								
							 | 
							
								% the rest of the word, can take zero or one argument.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartWORDCAPSTYLE{\MakeUppercase}
							 | 
						
						
						
							| 
								
							 | 
							
								% This is the horizontal separation distance from the drop letter to the main text.
							 | 
						
						
						
							| 
								
							 | 
							
								% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced
							 | 
						
						
						
							| 
								
							 | 
							
								% to the font that is active when \IEEEPARstart is called. 
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartSEP{0.15em}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 horizontal offset applied to the left of the drop cap.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartHOFFSET{0em}
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 Italic correction command applied at the end of the drop cap.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartITLCORRECT{\/}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compoc uses nonbold drop cap and small caps word style
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartFONTSTYLE{\mdseries}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartWORDFONTSTYLE{\scshape}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartWORDCAPSTYLE{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% definition of \IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% The token \@IEEEPARstartfont will be globally defined after the first use
							 | 
						
						
						
							| 
								
							 | 
							
								% of \IEEEPARstart and will be a font command which creates the big letter
							 | 
						
						
						
							| 
								
							 | 
							
								% The first argument is the first letter of the first word and the second
							 | 
						
						
						
							| 
								
							 | 
							
								% argument is the rest of the first word(s).
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEPARstart#1#2{\par{%
							 | 
						
						
						
							| 
								
							 | 
							
								% if this page does not have enough space, break it and lets start
							 | 
						
						
						
							| 
								
							 | 
							
								% on a new one
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtranneedspace{\@IEEEPARstartMINPAGELINES\baselineskip}{\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 move this up here in case user uses \textbf for \@IEEEPARstartFONTSTYLE
							 | 
						
						
						
							| 
								
							 | 
							
								% which uses command \leavevmode which causes an unwanted \indent to be issued
							 | 
						
						
						
							| 
								
							 | 
							
								\noindent
							 | 
						
						
						
							| 
								
							 | 
							
								% calculate the desired height of the big letter
							 | 
						
						
						
							| 
								
							 | 
							
								% it extends from the top of \@IEEEPARstartHEIGHTTEXT in the current font
							 | 
						
						
						
							| 
								
							 | 
							
								% down to \@IEEEPARstartDROPDEPTH below the current baseline
							 | 
						
						
						
							| 
								
							 | 
							
								\settoheight{\@IEEEtrantmpdimenA}{\@IEEEPARstartHEIGHTTEXT}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addtolength{\@IEEEtrantmpdimenA}{\@IEEEPARstartDROPDEPTH}%
							 | 
						
						
						
							| 
								
							 | 
							
								% extract the name of the current font in bold
							 | 
						
						
						
							| 
								
							 | 
							
								% and place it in \@IEEEPARstartFONTNAME
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\@IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%
							 | 
						
						
						
							| 
								
							 | 
							
								\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% define a font based on this name with a point size equal to the desired
							 | 
						
						
						
							| 
								
							 | 
							
								% height of the drop letter
							 | 
						
						
						
							| 
								
							 | 
							
								\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% save this value as a counter (integer) value (sp points)
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%
							 | 
						
						
						
							| 
								
							 | 
							
								% now get the height of the actual letter produced by this font size
							 | 
						
						
						
							| 
								
							 | 
							
								\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\@IEEEPARstartCAPSTYLE{#1}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% If something bogus happens like the first argument is empty or the
							 | 
						
						
						
							| 
								
							 | 
							
								% current font is strange, do not allow a zero height.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim\@IEEEtrantmpdimenB=0pt\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{ Forcing the drop letter font size to 10pt.}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenB=10pt%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% and store it as a counter
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%
							 | 
						
						
						
							| 
								
							 | 
							
								% Since a font size doesn't exactly correspond to the height of the capital
							 | 
						
						
						
							| 
								
							 | 
							
								% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,
							 | 
						
						
						
							| 
								
							 | 
							
								% will be less than that desired, \@IEEEtrantmpcountA
							 | 
						
						
						
							| 
								
							 | 
							
								% we need to raise the font size, \@IEEEtrantmpdimenA 
							 | 
						
						
						
							| 
								
							 | 
							
								% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB
							 | 
						
						
						
							| 
								
							 | 
							
								% But, TeX doesn't have floating point division, so we have to use integer
							 | 
						
						
						
							| 
								
							 | 
							
								% division. Hence the use of the counters.
							 | 
						
						
						
							| 
								
							 | 
							
								% We need to reduce the denominator so that the loss of the remainder will
							 | 
						
						
						
							| 
								
							 | 
							
								% have minimal affect on the accuracy of the result
							 | 
						
						
						
							| 
								
							 | 
							
								\divide\@IEEEtrantmpcountB by 200%
							 | 
						
						
						
							| 
								
							 | 
							
								\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%
							 | 
						
						
						
							| 
								
							 | 
							
								% Then reequalize things when we use TeX's ability to multiply by
							 | 
						
						
						
							| 
								
							 | 
							
								% floating point values
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%
							 | 
						
						
						
							| 
								
							 | 
							
								\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%
							 | 
						
						
						
							| 
								
							 | 
							
								% \@IEEEPARstartfont is globaly set to the calculated font of the big letter
							 | 
						
						
						
							| 
								
							 | 
							
								% We need to carry this out of the local calculation area to to create the
							 | 
						
						
						
							| 
								
							 | 
							
								% big letter.
							 | 
						
						
						
							| 
								
							 | 
							
								\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%
							 | 
						
						
						
							| 
								
							 | 
							
								% Now set \@IEEEtrantmpdimenA to the width of the big letter
							 | 
						
						
						
							| 
								
							 | 
							
								% We need to carry this out of the local calculation area to set the
							 | 
						
						
						
							| 
								
							 | 
							
								% hanging indent
							 | 
						
						
						
							| 
								
							 | 
							
								\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% end of the isolated calculation environment
							 | 
						
						
						
							| 
								
							 | 
							
								% add in the extra clearance we want
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% add in the optional offset
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpdimenA by \@IEEEPARstartHOFFSET\relax%
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 don't allow negative offsets to produce negative hanging indents
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% \@IEEEtrantmpdimenA has the width of the big letter plus the
							 | 
						
						
						
							| 
								
							 | 
							
								% separation space and \@IEEEPARstartfont is the font we need to use
							 | 
						
						
						
							| 
								
							 | 
							
								% Now, we make the letter and issue the hanging indent command
							 | 
						
						
						
							| 
								
							 | 
							
								% The letter is placed in a box of zero width and height so that other
							 | 
						
						
						
							| 
								
							 | 
							
								% text won't be displaced by it.
							 | 
						
						
						
							| 
								
							 | 
							
								\hangindent\@IEEEtrantmpdimenB\hangafter=-\@IEEEPARstartDROPLINES%
							 | 
						
						
						
							| 
								
							 | 
							
								\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}%
							 | 
						
						
						
							| 
								
							 | 
							
								\raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\@IEEEPARstartHOFFSET}%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEPARstartfont\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}%
							 | 
						
						
						
							| 
								
							 | 
							
								\hspace{\@IEEEPARstartSEP}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								{\@IEEEPARstartWORDFONTSTYLE{\@IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% determines if the space remaining on a given page is equal to or greater
							 | 
						
						
						
							| 
								
							 | 
							
								% than the specified space of argument one
							 | 
						
						
						
							| 
								
							 | 
							
								% if not, execute argument two (only if the remaining space is greater than zero)
							 | 
						
						
						
							| 
								
							 | 
							
								% and issue a \newpage
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% example: \@IEEEtranneedspace{2in}{\vfill}
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% Does not take into consideration rubber shrinkage, so it tends to
							 | 
						
						
						
							| 
								
							 | 
							
								% be overly cautious
							 | 
						
						
						
							| 
								
							 | 
							
								% Based on an example posted by Donald Arseneau
							 | 
						
						
						
							| 
								
							 | 
							
								% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,
							 | 
						
						
						
							| 
								
							 | 
							
								% so DO NOT PASS \@IEEEtrantmpdimenB to this routine
							 | 
						
						
						
							| 
								
							 | 
							
								% if you need a dimen register, import with \@IEEEtrantmpdimenA instead
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left
							 | 
						
						
						
							| 
								
							 | 
							
								\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\newpage%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi\endgroup}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEEbiography ENVIRONMENT
							 | 
						
						
						
							| 
								
							 | 
							
								% Allows user to enter biography leaving place for picture (adapts to font size)
							 | 
						
						
						
							| 
								
							 | 
							
								% As of V1.5, a new optional argument allows you to have a real graphic!
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.5 and later also fixes the "colliding biographies" which could happen when a 
							 | 
						
						
						
							| 
								
							 | 
							
								% biography's text was shorter than the space for the photo.
							 | 
						
						
						
							| 
								
							 | 
							
								% MDS 7/2001
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 prevent multiple biographies from making multiple TOC entries
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEbiographyTOCentrynotmade
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEbiographyTOCentrynotmadetrue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% biography counter so hyperref can jump directly to the biographies
							 | 
						
						
						
							| 
								
							 | 
							
								% and not just the previous section
							 | 
						
						
						
							| 
								
							 | 
							
								\newcounter{IEEEbiography}
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{IEEEbiography}{0}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% photo area size
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBIOphotowidth{1.0in}    % width of the biography photo area
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBIOphotodepth{1.25in}   % depth (height) of the biography photo area
							 | 
						
						
						
							| 
								
							 | 
							
								% area cleared for photo
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBIOhangwidth{1.14in}    % width cleared for the biography photo area
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBIOhangdepth{1.25in}    % depth cleared for the biography photo area
							 | 
						
						
						
							| 
								
							 | 
							
								                                  % actual depth will be a multiple of 
							 | 
						
						
						
							| 
								
							 | 
							
								                                  % \baselineskip, rounded up
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{IEEEbiography}[2][]{\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize%
							 | 
						
						
						
							| 
								
							 | 
							
								\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%
							 | 
						
						
						
							| 
								
							 | 
							
								% we need enough space to support the hanging indent
							 | 
						
						
						
							| 
								
							 | 
							
								% the nominal value of the spacer
							 | 
						
						
						
							| 
								
							 | 
							
								% and one extra line for good measure
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpdimenA by 1\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								% if this page does not have enough space, break it and lets start
							 | 
						
						
						
							| 
								
							 | 
							
								% with a new one
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%
							 | 
						
						
						
							| 
								
							 | 
							
								% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill
							 | 
						
						
						
							| 
								
							 | 
							
								\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								% the default box for where the photo goes
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{%
							 | 
						
						
						
							| 
								
							 | 
							
								\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% detect if the optional argument was supplied, this requires the
							 | 
						
						
						
							| 
								
							 | 
							
								% \@ifmtarg command as defined in the appendix section above
							 | 
						
						
						
							| 
								
							 | 
							
								% and if so, override the default box with what they want
							 | 
						
						
						
							| 
								
							 | 
							
								\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%
							 | 
						
						
						
							| 
								
							 | 
							
								\centering%
							 | 
						
						
						
							| 
								
							 | 
							
								#1%
							 | 
						
						
						
							| 
								
							 | 
							
								\end{minipage}}}}% end if optional argument supplied
							 | 
						
						
						
							| 
								
							 | 
							
								% Make an entry into the table of contents only if we have not done so before
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEbiographyTOCentrynotmade%
							 | 
						
						
						
							| 
								
							 | 
							
								% link labels to the biography counter so hyperref will jump
							 | 
						
						
						
							| 
								
							 | 
							
								% to the biography, not the previous section
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{IEEEbiography}{-1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\refstepcounter{IEEEbiography}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{section}{Biographies}%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEbiographyTOCentrynotmadefalse%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% one more biography
							 | 
						
						
						
							| 
								
							 | 
							
								\refstepcounter{IEEEbiography}%
							 | 
						
						
						
							| 
								
							 | 
							
								% Make an entry for this name into the table of contents 
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{subsection}{#2}%
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 properly handle if a new paragraph should occur while the
							 | 
						
						
						
							| 
								
							 | 
							
								% hanging indent is still active. Do this by redefining \par so
							 | 
						
						
						
							| 
								
							 | 
							
								% that it will not start a new paragraph. (But it will appear to the
							 | 
						
						
						
							| 
								
							 | 
							
								% user as if it did.) Also, strip any leading pars, newlines, or spaces.
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEEBIOORGparCMD=\par% save the original \par command
							 | 
						
						
						
							| 
								
							 | 
							
								\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par
							 | 
						
						
						
							| 
								
							 | 
							
								\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth
							 | 
						
						
						
							| 
								
							 | 
							
								\divide\@IEEEtrantmpcountA by \baselineskip%  calculates lines needed to produce the hang depth
							 | 
						
						
						
							| 
								
							 | 
							
								\advance\@IEEEtrantmpcountA by 1% ensure we overestimate
							 | 
						
						
						
							| 
								
							 | 
							
								% set the hanging indent
							 | 
						
						
						
							| 
								
							 | 
							
								\hangindent\@IEEEBIOhangwidth%
							 | 
						
						
						
							| 
								
							 | 
							
								\hangafter-\@IEEEtrantmpcountA%
							 | 
						
						
						
							| 
								
							 | 
							
								% reference the top of the photo area to the top of a capital T
							 | 
						
						
						
							| 
								
							 | 
							
								\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% set the photo box, give it zero width and height so as not to disturb anything
							 | 
						
						
						
							| 
								
							 | 
							
								\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{%
							 | 
						
						
						
							| 
								
							 | 
							
								\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								% now place the author name and begin the bio text
							 | 
						
						
						
							| 
								
							 | 
							
								\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%
							 | 
						
						
						
							| 
								
							 | 
							
								% 7/2001 V1.5 detect when the biography text is shorter than the photo area
							 | 
						
						
						
							| 
								
							 | 
							
								% and pad the unused area - preventing a collision from the next biography entry
							 | 
						
						
						
							| 
								
							 | 
							
								% MDS
							 | 
						
						
						
							| 
								
							 | 
							
								\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad
							 | 
						
						
						
							| 
								
							 | 
							
								    \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line
							 | 
						
						
						
							| 
								
							 | 
							
								    \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding
							 | 
						
						
						
							| 
								
							 | 
							
								    \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%
							 | 
						
						
						
							| 
								
							 | 
							
								    \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								\par\normalfont}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6
							 | 
						
						
						
							| 
								
							 | 
							
								% added biography without a photo environment
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{IEEEbiographynophoto}[1]{%
							 | 
						
						
						
							| 
								
							 | 
							
								% Make an entry into the table of contents only if we have not done so before
							 | 
						
						
						
							| 
								
							 | 
							
								\if@IEEEbiographyTOCentrynotmade%
							 | 
						
						
						
							| 
								
							 | 
							
								% link labels to the biography counter so hyperref will jump
							 | 
						
						
						
							| 
								
							 | 
							
								% to the biography, not the previous section
							 | 
						
						
						
							| 
								
							 | 
							
								\setcounter{IEEEbiography}{-1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\refstepcounter{IEEEbiography}%
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{section}{Biographies}%
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEbiographyTOCentrynotmadefalse%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi%
							 | 
						
						
						
							| 
								
							 | 
							
								% one more biography
							 | 
						
						
						
							| 
								
							 | 
							
								\refstepcounter{IEEEbiography}%
							 | 
						
						
						
							| 
								
							 | 
							
								% Make an entry for this name into the table of contents 
							 | 
						
						
						
							| 
								
							 | 
							
								\addcontentsline{toc}{subsection}{#1}%
							 | 
						
						
						
							| 
								
							 | 
							
								\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize\interlinepenalty500%
							 | 
						
						
						
							| 
								
							 | 
							
								\vskip 4\baselineskip plus 1fil minus 0\baselineskip%
							 | 
						
						
						
							| 
								
							 | 
							
								\parskip=0pt\par%
							 | 
						
						
						
							| 
								
							 | 
							
								\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide the user with some old font commands
							 | 
						
						
						
							| 
								
							 | 
							
								% got this from article.cls
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
							 | 
						
						
						
							| 
								
							 | 
							
								\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% SPECIAL PAPER NOTICE COMMANDS
							 | 
						
						
						
							| 
								
							 | 
							
								% 
							 | 
						
						
						
							| 
								
							 | 
							
								% holds the special notice text
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEspecialpapernotice{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								 
							 | 
						
						
						
							| 
								
							 | 
							
								% for special papers, like invited papers, the user can do:
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEspecialpapernotice{(Invited Paper)} before \maketitle
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEspecialpapernotice#1{\ifCLASSOPTIONconference%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEspecialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\else%
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEspecialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%
							 | 
						
						
						
							| 
								
							 | 
							
								\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% PUBLISHER ID COMMANDS
							 | 
						
						
						
							| 
								
							 | 
							
								% to insert a publisher's ID footer
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 \IEEEpubid has been changed so that the change in page size and style
							 | 
						
						
						
							| 
								
							 | 
							
								% occurs in \maketitle. \IEEEpubid must now be issued prior to \maketitle
							 | 
						
						
						
							| 
								
							 | 
							
								% use \IEEEpubidadjcol as before - in the second column of the title page
							 | 
						
						
						
							| 
								
							 | 
							
								% These changes allow \maketitle to take the reduced page height into
							 | 
						
						
						
							| 
								
							 | 
							
								% consideration when dynamically setting the space between the author 
							 | 
						
						
						
							| 
								
							 | 
							
								% names and the maintext.
							 | 
						
						
						
							| 
								
							 | 
							
								%
							 | 
						
						
						
							| 
								
							 | 
							
								% the amount the main text is pulled up to make room for the
							 | 
						
						
						
							| 
								
							 | 
							
								% publisher's ID footer
							 | 
						
						
						
							| 
								
							 | 
							
								% IEEE uses about 1.3\baselineskip for journals, 
							 | 
						
						
						
							| 
								
							 | 
							
								% dynamic title spacing will clean up the fraction
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEpubidpullup{1.3\baselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote
							 | 
						
						
						
							| 
								
							 | 
							
								% for technotes it must be an integer of baselineskip as there can be no
							 | 
						
						
						
							| 
								
							 | 
							
								% dynamic title spacing for two column mode technotes (the title is in the
							 | 
						
						
						
							| 
								
							 | 
							
								% in first column) and we should maintain an integer number of lines in the
							 | 
						
						
						
							| 
								
							 | 
							
								% second column
							 | 
						
						
						
							| 
								
							 | 
							
								% There are some examples (such as older issues of "Transactions on
							 | 
						
						
						
							| 
								
							 | 
							
								% Information Theory") in which IEEE really pulls the text off the ID for
							 | 
						
						
						
							| 
								
							 | 
							
								% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip
							 | 
						
						
						
							| 
								
							 | 
							
								% and call it even.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEpubidpullup{2\baselineskip}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 compsoc does not use a pullup
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONcompsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEpubidpullup{0pt}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% holds the ID text
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEEpubid{\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flag so \maketitle can tell if \IEEEpubid was called
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEusingpubid
							 | 
						
						
						
							| 
								
							 | 
							
								\global\@IEEEusingpubidfalse
							 | 
						
						
						
							| 
								
							 | 
							
								% issue this command in the page to have the ID at the bottom
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.6 use before \maketitle
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpubid#1{\def\@IEEEpubid{#1}\global\@IEEEusingpubidtrue}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% command which will pull up (shorten) the column it is executed in
							 | 
						
						
						
							| 
								
							 | 
							
								% to make room for the publisher ID. Place in the second column of
							 | 
						
						
						
							| 
								
							 | 
							
								% the title page when using \IEEEpubid
							 | 
						
						
						
							| 
								
							 | 
							
								% Is smart enough not to do anything when in single column text or
							 | 
						
						
						
							| 
								
							 | 
							
								% if the user hasn't called \IEEEpubid
							 | 
						
						
						
							| 
								
							 | 
							
								% currently needed in for the second column of a page with the
							 | 
						
						
						
							| 
								
							 | 
							
								% publisher ID. If not needed in future releases, please provide this
							 | 
						
						
						
							| 
								
							 | 
							
								% command and define it as \relax for backward compatibility
							 | 
						
						
						
							| 
								
							 | 
							
								% v1.6b do not allow command to operate if the peer review option has been 
							 | 
						
						
						
							| 
								
							 | 
							
								% selected because \IEEEpubidadjcol will not be on the cover page.
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 do nothing if compsoc
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpubidadjcol{\ifCLASSOPTIONcompsoc\else\ifCLASSOPTIONpeerreview\else
							 | 
						
						
						
							| 
								
							 | 
							
								\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@IEEEpubidpullup}\fi\fi\fi\fi}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% Special thanks to Peter Wilson, Daniel Luecking, and the other
							 | 
						
						
						
							| 
								
							 | 
							
								% gurus at comp.text.tex, for helping me to understand how best to
							 | 
						
						
						
							| 
								
							 | 
							
								% implement the IEEEpubid command in LaTeX.
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% Lockout some commands under various conditions
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% general purpose bit bucket
							 | 
						
						
						
							| 
								
							 | 
							
								\newsavebox{\@IEEEtranrubishbin}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% flags to prevent multiple warning messages
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNthanks
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEbiography
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEbiographynophoto
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEpubid
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEpubidadjcol
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEmembership
							 | 
						
						
						
							| 
								
							 | 
							
								\newif\if@IEEEWARNIEEEaftertitletext
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNthankstrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEPARstarttrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEbiographytrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEbiographynophototrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEpubidtrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEpubidadjcoltrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEmembershiptrue
							 | 
						
						
						
							| 
								
							 | 
							
								\@IEEEWARNIEEEaftertitletexttrue
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%% Lockout some commands when in various modes, but allow them to be restored if needed
							 | 
						
						
						
							| 
								
							 | 
							
								%%
							 | 
						
						
						
							| 
								
							 | 
							
								% save commands which might be locked out
							 | 
						
						
						
							| 
								
							 | 
							
								% so that the user can later restore them if needed
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDthanks\thanks
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEPARstart\IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEbiography\IEEEbiography
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDendIEEEbiography\endIEEEbiography
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEbiographynophoto\IEEEbiographynophoto
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDendIEEEbiographynophoto\endIEEEbiographynophoto
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEpubid\IEEEpubid
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEpubidadjcol\IEEEpubidadjcol
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEmembership\IEEEmembership
							 | 
						
						
						
							| 
								
							 | 
							
								\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% disable \IEEEPARstart when in draft mode
							 | 
						
						
						
							| 
								
							 | 
							
								% This may have originally been done because the pre-V1.6 drop letter
							 | 
						
						
						
							| 
								
							 | 
							
								% algorithm had problems with a non-unity baselinestretch
							 | 
						
						
						
							| 
								
							 | 
							
								% At any rate, it seems too formal to have a drop letter in a draft
							 | 
						
						
						
							| 
								
							 | 
							
								% paper.
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONdraftcls
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** ATTENTION: \noexpand\IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								 is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								% and for technotes
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONtechnote
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% lockout unneeded commands when in conference mode
							 | 
						
						
						
							| 
								
							 | 
							
								\ifCLASSOPTIONconference
							 | 
						
						
						
							| 
								
							 | 
							
								% when locked out, \thanks, \IEEEbiography, \IEEEbiographynophoto, \IEEEpubid,
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEmembership and \IEEEaftertitletext will all swallow their given text. 
							 | 
						
						
						
							| 
								
							 | 
							
								% \IEEEPARstart will output a normal character instead
							 | 
						
						
						
							| 
								
							 | 
							
								% warn the user about these commands only once to prevent the console screen
							 | 
						
						
						
							| 
								
							 | 
							
								% from filling up with redundant messages
							 | 
						
						
						
							| 
								
							 | 
							
								\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% LaTeX treats environments and commands with optional arguments differently.
							 | 
						
						
						
							| 
								
							 | 
							
								% the actual ("internal") command is stored as \\commandname 
							 | 
						
						
						
							| 
								
							 | 
							
								% (accessed via \csname\string\commandname\endcsname )
							 | 
						
						
						
							| 
								
							 | 
							
								% the "external" command \commandname is a macro with code to determine
							 | 
						
						
						
							| 
								
							 | 
							
								% whether or not the optional argument is presented and to provide the 
							 | 
						
						
						
							| 
								
							 | 
							
								% default if it is absent. So, in order to save and restore such a command
							 | 
						
						
						
							| 
								
							 | 
							
								% we would have to save and restore \\commandname as well. But, if LaTeX
							 | 
						
						
						
							| 
								
							 | 
							
								% ever changes the way it names the internal names, the trick would break.
							 | 
						
						
						
							| 
								
							 | 
							
								% Instead let us just define a new environment so that the internal
							 | 
						
						
						
							| 
								
							 | 
							
								% name can be left undisturbed.
							 | 
						
						
						
							| 
								
							 | 
							
								\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNIEEEbiography\typeout{** WARNING: \noexpand\IEEEbiography
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographyfalse%
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								% and make biography point to our bogus biography
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEbiography=\@IEEEbogusbiography
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endIEEEbiography=\end@IEEEbogusbiography
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\renewenvironment{IEEEbiographynophoto}[1]{\if@IEEEWARNIEEEbiographynophoto\typeout{** WARNING: \noexpand\IEEEbiographynophoto
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographynophotofalse%
							 | 
						
						
						
							| 
								
							 | 
							
								\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpubid#1{\if@IEEEWARNIEEEpubid\typeout{** WARNING: \noexpand\IEEEpubid 
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEpubidadjcol{\if@IEEEWARNIEEEpubidadjcol\typeout{** WARNING: \noexpand\IEEEpubidadjcol
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidadjcolfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext
							 | 
						
						
						
							| 
								
							 | 
							
								 is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}
							 | 
						
						
						
							| 
								
							 | 
							
								\fi
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide a way to restore the commands that are locked out
							 | 
						
						
						
							| 
								
							 | 
							
								\def\IEEEoverridecommandlockouts{%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\thanks\@IEEESAVECMDthanks%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEPARstart\@IEEESAVECMDIEEEPARstart%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEbiography\@IEEESAVECMDIEEEbiography%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endIEEEbiography\@IEEESAVECMDendIEEEbiography%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEbiographynophoto\@IEEESAVECMDIEEEbiographynophoto%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\endIEEEbiographynophoto\@IEEESAVECMDendIEEEbiographynophoto%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEpubid\@IEEESAVECMDIEEEpubid%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEpubidadjcol\@IEEESAVECMDIEEEpubidadjcol%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEmembership\@IEEESAVECMDIEEEmembership%
							 | 
						
						
						
							| 
								
							 | 
							
								\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% need a backslash character for typeout output
							 | 
						
						
						
							| 
								
							 | 
							
								{\catcode`\|=0 \catcode`\\=12
							 | 
						
						
						
							| 
								
							 | 
							
								|xdef|@IEEEbackslash{\}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% hook to allow easy disabling of all legacy warnings
							 | 
						
						
						
							| 
								
							 | 
							
								\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno).
							 | 
						
						
						
							| 
								
							 | 
							
								Use \@IEEEbackslash #2 instead.}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide for legacy commands
							 | 
						
						
						
							| 
								
							 | 
							
								\def\authorblockA{\@IEEElegacywarn{authorblockA}{IEEEauthorblockA}\IEEEauthorblockA}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\authorblockN{\@IEEElegacywarn{authorblockN}{IEEEauthorblockN}\IEEEauthorblockN}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\authorrefmark{\@IEEElegacywarn{authorrefmark}{IEEEauthorrefmark}\IEEEauthorrefmark}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\pubid{\@IEEElegacywarn{pubid}{IEEEpubid}\IEEEpubid}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\pubidadjcol{\@IEEElegacywarn{pubidadjcol}{IEEEpubidadjcol}\IEEEpubidadjcol}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\QED{\@IEEElegacywarn{QED}{IEEEQED}\IEEEQED}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\QEDclosed{\@IEEElegacywarn{QEDclosed}{IEEEQEDclosed}\IEEEQEDclosed}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\QEDopen{\@IEEElegacywarn{QEDopen}{IEEEQEDopen}\IEEEQEDopen}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\specialpapernotice{\@IEEElegacywarn{specialpapernotice}{IEEEspecialpapernotice}\IEEEspecialpapernotice}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide for legacy environments
							 | 
						
						
						
							| 
								
							 | 
							
								\def\biography{\@IEEElegacywarn{biography}{IEEEbiography}\IEEEbiography}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\biographynophoto{\@IEEElegacywarn{biographynophoto}{IEEEbiographynophoto}\IEEEbiographynophoto}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\keywords{\@IEEElegacywarn{keywords}{IEEEkeywords}\IEEEkeywords}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endbiography{\endIEEEbiography}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endbiographynophoto{\endIEEEbiographynophoto}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\endkeywords{\endIEEEkeywords}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% provide for legacy IED commands/lengths when possible
							 | 
						
						
						
							| 
								
							 | 
							
								\let\labelindent\IEEElabelindent
							 | 
						
						
						
							| 
								
							 | 
							
								\def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl}
							 | 
						
						
						
							| 
								
							 | 
							
								\def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% let \proof use the IEEEtran version even after amsthm is loaded
							 | 
						
						
						
							| 
								
							 | 
							
								% \proof is now deprecated in favor of \IEEEproof
							 | 
						
						
						
							| 
								
							 | 
							
								\AtBeginDocument{\def\proof{\@IEEElegacywarn{proof}{IEEEproof}\IEEEproof}\def\endproof{\endIEEEproof}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								% V1.7 \overrideIEEEmargins is no longer supported.
							 | 
						
						
						
							| 
								
							 | 
							
								\def\overrideIEEEmargins{%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{** WARNING: \string\overrideIEEEmargins \space no longer supported (line \the\inputlineno).}%
							 | 
						
						
						
							| 
								
							 | 
							
								\typeout{** Use the \string\CLASSINPUTinnersidemargin, \string\CLASSINPUToutersidemargin \space controls instead.}}
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								\endinput
							 | 
						
						
						
							| 
								
							 | 
							
								
							 | 
						
						
						
							| 
								
							 | 
							
								%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls  %%%%%%%%%%%%%%%%%%%%%%%%%%%%
							 | 
						
						
						
							| 
								
							 | 
							
								% That's all folks!
							 | 
						
						
						
							| 
								
							 | 
							
								
							 |