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-%% This is sodaptex.all. This file is to be used for creating a paper
-%% in the ACM/SIAM Preprint series with Plain TeX. It consists of the following
-%% two files:
-%%
-%% ptexpprt.tex ---- an example and documentation file
-%% ptexpprt.sty ---- the macro file
-%%
-%% To use, cut this file apart at the appropriate places. You can run the
-%% example file with the macros to get sample output.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is ptexpprt.tex, an example file for use with the ACM/SIAM Plain TeX
-% Preprint Series macros. It is designed to produce double-column output.
-% Comments are placed at the beginning and throughout this file. Please
-% take the time to read them as they document how to use these macros.
-% This file can be composed and printed out for use as sample output.
-
-% Any comments or questions regarding these macros should be directed to:
-%
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-
-% This file is to be used as an example for style only. It should not be read
-% for content.
-
-%%%%%%%%%%%%%%% PLEASE NOTE THE FOLLOWING STYLE RESTRICTIONS %%%%%%%%%%%%%%%
-
-%% 1. You must use the numbered reference style([1],[2]), listing the
-%% references at the end of the chapter either by order of citation
-%% or alphabetically.
-%%
-%% 2. Unless otherwise stated by your editor, do your chapter as if it
-%% is Chapter 1.
-%% If you know which number your chapter is, you must do the following:
-%%
-%% Go into the style file (ptexfrnt.sty) and search for the
-%% \def\chapter#1 definition. At the end of this definition
-%% there is a command \headcount=1. Change the 1 to
-%% the appropriate number. This change will cause the headings
-%% in your chapter to match the chapter number.
-%%
-%% 3. This macro is set up for two levels of headings. The macro will
-%% automatically number the headings for you.
-%%
-%% 4. The running heads are defined in the output routine. It will be
-%% necessary for you to alter the information currently included.
-%% To do this, go into the style file and search for OUTPUT. Once there,
-%% scroll through the file until you see the command \def\rhead. Replace
-%% CHAPTER TITLE with the title (or shortened title) of your paper.
-%% Replace AUTHORS NAMES with the appropriate names.
-%% Neither running head may be longer than 50 characters.
-%%
-%% 5. Theorems, Lemmas, Definitions, etc. are to be triple numbered,
-%% indicating the chapter, section, and the occurence of that element
-%% within that section. (For example, the first theorem in the second
-%% section of chapter three would be numbered 3.2.1. This numbering must
-%% be done manually.
-%%
-%% 6. Figures and equations must be manually double-numbered, indicating
-%% chapter and occurence. Use \leqno for equation numbering. See the
-%% example of \caption for figure numbering.
-%% Note. Although not shown, tables must also be double-numbered. The
-%% command \caption can also be used for table captions.
-%%
-%% 7. At the first occurence of each new element there is a description
-%% of how to use the coding.
-%%
-%%%%%%% PLEASE NOTE THE FOLLOWING POTENTIAL PROBLEMS:
-%
-%% 1. A bug exists that prevents a page number from printing on the first
-%% page of the paper. Please ignore this problem. It will be handled
-%% after you submit your paper.
-%%
-%% 2. The use of \topinsert and \midinsert to allow space for figures can
-%% result in unusual page breaks, or unusual looking pages in general.
-%% If you encounter such a situation, contact the SIAM office at the
-%% address listed above for instructions.
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\input ptexpprt.sty
-\voffset=.25in
-\titlepage
-
-% It will be necessary to hard code the chapter title and chapter authors.
-% You must decide where to break the lines. For the authors, please follow
-% the following conventions:
-% 1. If 2 authors are on a line, use \hskip4pc between them. If 3 authors,
-% use \hskip2pc. Do not put more than 3 authors on the same line.
-% 2. Use the following notation: asterisk, dagger, double-dagger, section
-% symbol, paragraph symbol, double asterisk. If more are needed, contact
-% the SIAM office.
-
-\centerline{\chapterfont Chapter 1}
-\vskip2pt
-\centerline{\titlefont SIAM/ACM Preprint Series Macros for
-Plain TeX\footnote*{Supported by GSF grants ABC123, DEF456, and GHI 789.}}
-\vskip15pt
-\centerline{\authorfont J. Corey Gray\footnote\dag{Society for Industrial and
-Applied Mathematics.}\hskip2pc Tricia Manning\footnote\ddag{Society for
-Industrial and Applied Mathematics.}\hskip2pc Vickie Kearn\footnote\S{Society
-for Industrial and Applied Mathematics.}}
-\vskip2pc
-
-\begindoublecolumns
-
-% Use \headone for the first level headings. The macro will automatically
-% number the headings.
-
-\headone{Problem Specification}
-In this paper, we consider the solution of the $N \times N$ linear
-system
-$$A x = b\leqno(1.1)$$
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-$$
-P A P^{t} = L D L^{t}
-$$
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headtwo{Robustness}In \S 1.2, we review the bordering algorithm, and introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-
-
-% Use \thm and \endthm for theorems. They must be numbered manually.
-% Lemmas (\lem \endlem), corollaries (\cor \endcor), and
-% propositions (\prop \endprop) are coded the same as theorems and must
-% also be numbered manually.
-
-\thm{Theorem 2.1.} The method was extended to three
-dimensions. For the standard multigrid
-coarsening
-(in which, for a given grid, the next coarser grid has $1/8$
-as many points), anisotropic problems require plane
-relaxation to
-obtain a good smoothing factor.\endthm
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \prf to begin a proof.
-
-\prf{Proof} In this paper we consider two methods. The first method
-is
-basically the method considered with two differences:
-first, we perform plane relaxation by a two-dimensional
-multigrid method, and second, we use a slightly different
-choice of
-interpolation operator, which improves performance
-for nearly singular problems. In the second method coarsening
-is done by successively coarsening each.
-
-% Use \dfn to begin definitions.
-
-\dfn{Definition 1.2.1.}We describe the two methods in \S\ 1.2. This is a
-definition in the plain tex macro.
-
-This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-% Use \midinsert along with \caption to allow space for
-% figures. See note above in problem section.
-%\midinsert\vskip15.5pc\caption{Fig. 1.1. {\nineit This is figure 1.}}
-% \endcaption\endinsert
-
-In this paper, we consider the solution of the $N \times N$ linear
-system
-where $A$ is large, sparse, symmetric, and positive definite. We consider
-the direct solution of by means of general sparse Gaussian
-elimination. In such a procedure, we find a permutation matrix $P$, and
-compute the decomposition
-where $L$ is unit lower triangular and $D$ is diagonal.
-
-\headone{Design Considerations}
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Several good ordering algorithms (nested dissection and minimum degree)
-are available for computing $P$ [1], [2].
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-Our purpose here is to examine the nonnumerical complexity of the
-sparse elimination algorithm given in [3].
-As was shown there, a general sparse elimination scheme based on the
-bordering algorithm requires less storage for pointers and
-row/column indices than more traditional implementations of general
-sparse elimination. This is accomplished by exploiting the m-tree,
-a particular spanning tree for the graph of the filled-in matrix.
-Since our interest here does not
-focus directly on the ordering, we assume for convenience that $P=I$,
-or that $A$ has been preordered to reflect an appropriate choice of $P$.
-
-% Use \lem and \endlem to begin and end lemmas.
-
-\lem{Lemma 2.1.}We discuss first the choice for $I_{k-1}^k$
-which is a generalization. We assume that $G^{k-1}$ is
-obtained
-from $G^k$
-by standard coarsening; that is, if $G^k$ is a tensor product
-grid $G_{x}^k \times G_{y}^k \times G_{z}^k$,
-$G^{k-1}=G_{x}^{k-1} \times G_{y}^{k-1} \times G_{z}^{k-1}$,
-where $G_{x}^{k-1}$ is obtained by deleting every other grid
-point of $G_x^k$ and similarly for $G_{y}^k$ and $G_{z}^k$.
-\endlem
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% Use \headtwo for second level headings. They will be numbered automatically.
-
-\headone{Problem Solving}In \S 1.2, we review the bordering algorithm, and
-introduce
-the sorting and intersection problems that arise in the
-sparse formulation of the algorithm.
-
-\headtwo{Versatility} In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-
-\headtwo{Complexity}For the old approach, we show that the
-complexity of the intersection problem is $O(n^{3})$, the same
-as the complexity of the numerical computations. For the
-new approach, the complexity of the second part is reduced to
-$O(n^{2} (\log n)^{2})$.
-
-To our knowledge, the m-tree previously has not been applied in this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6]. In \S 1.3., we analyze the complexity of the old and new
-approaches to the intersection problem for the special case of
-an $n \times n$ grid ordered by nested dissection. The special
-structure of this problem allows us to make exact estimates of
-the complexity. To our knowledge, the m-tree previously has not been applied in
-this
-fashion to the numerical factorization, but it has been used,
-directly or indirectly, in several optimal order algorithms for
-computing the fill-in during the symbolic factorization phase
-[4] - [10], [5], [6].
-
-% The command \Refs sets the word Reference as a heading and allows the proper
-% amount of space before the start of the references. Each reference must
-% begin with \ref\\. The article or title of the reference should be in
-% italic. Use the \it command within brackets. End each reference with
-% \endref and allow two returns between references. Use the command
-% \sameauthor (see reference 8) when the same author or group of authors
-% is listed consecutively.
-
-\Refs
-
-\ref 1\\R.~E. Bank, {\it PLTMG users' guide, edition 5.0}, tech. report,
- Department of Mathematics, University of California, San Diego, CA,
-1988.\endref
-
-\ref 2\\R.~E. Bank, T.~F. Dupont, and H.~Yserentant, {\it The hierarchical basis
- multigrid method}, Numer. Math., 52 (1988), pp.~427--458.\endref
-
-\ref 3\\R.~E. Bank and R.~K. Smith, {\it General sparse elimination requires no
- permanent integer storage}, SIAM J. Sci. Stat. Comput., 8 (1987),
- pp.~574--584.\endref
-
-\ref 4\\S.~C. Eisenstat, M.~C. Gursky, M.~Schultz, and A.~Sherman, {\it
- Algorithms and data structures for sparse symmetric gaussian elimination},
- SIAM J. Sci. Stat. Comput., 2 (1982), pp.~225--237.\endref
-
-\ref 5\\A.~George and J.~Liu, {\it Computer Solution of Large Positive
- Definite Systems}, Prentice Hall, Englewood Cliffs, NJ, 1981.\endref
-
-\ref 6\\K.~H. Law and S.~J. Fenves, {\it A node addition model for symbolic
- factorization}, ACM TOMS, 12 (1986), pp.~37--50.\endref
-
-\ref 7\\J.~W.~H. Liu, {\it A compact row storage scheme for factors
- using elimination trees}, ACM TOMS, 12 (1986), pp.~127--148.\endref
-
-\ref 8\\\sameauthor , {\it The role of
- elimination trees in sparse factorization}, Tech. Report CS-87-12,Department
- of Computer Science, York University, Ontario, Canada, 1987.\endref
-
-\ref 9\\D.~J. Rose, {\it A graph theoretic study of the numeric solution of
- sparse positive definite systems}, in Graph Theory and Computing,
- Academic Press, New York, 1972.\endref
-
-\ref 10\\D.~J. Rose, R.~E. Tarjan, and G.~S. Lueker, {\it Algorithmic aspects of
- vertex elimination on graphs}, SIAM J. Comput., 5 (1976), pp.~226--283.\endref
-\enddoublecolumns
-
-\bye
-%%
-%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%% ptexpprt.sty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% This is a file of macros and definitions for creating a chapter
-% for publication in the ACM/SIAM Preprint Series using Plain TeX.
-% This file may be freely distributed but may not be altered in any way.
-% Any comments or questions regarding these macros should be directed to:
-
-% Corey Gray
-% SIAM
-% 3600 University City Science Center
-% Philadelphia, PA 19104-2688
-% USA
-% Telephone: (215) 382-9800
-% Fax: (215) 386-7999
-% e-mail: gray@siam.org
-%
-
-% Report the version.
-\message{*** ACM/SIAM Plain TeX Preprint Series macro package, version 1.0,
-September 24, 1990.***}
-
-% Make the @ sign a letter for internal control sequences.
-\catcode`\@=11
-%
-%
-%
-
-
-
-%%% DIMENSIONS %%%
-
-\newdimen\pagewidth
-\hsize=41pc
-\pagewidth=\hsize
-\newdimen\pageheight
-\vsize=50pc
-\pageheight=\vsize
-\newdimen\ruleht
-\ruleht=.5pt
-\maxdepth=2.2pt
-
-\parindent=18truept
-\def\firstpar{\parindent=0pt\global\everypar{\parindent=18truept}}
-\parskip=0pt plus 1pt
-
-
-%%% FONTS %%%
-
-\font\tenrm=cmr10
-\font\tenbf=cmbx10
-\font\tenit=cmti10
-\font\tensmc=cmcsc10
-\def\tenpoint{%
- \def\rm{\tenrm}\def\bf{\tenbf}%
- \def\it{\tenit}\def\smc{\tensmc}
- \textfont0=\tenrm \scriptfont0=\sevenrm
- \textfont1=\teni \scriptfont1=\seveni
- \textfont2=\tensy \scriptfont2=\sevensy
- \textfont3=\tenex \scriptfont3=\tenex
-\baselineskip=12pt\rm}%
-
-\font\ninerm=cmr9
-\font\ninebf=cmbx9
-\font\nineit=cmti9
-\def\ninepoint{%
- \def\rm{\ninerm}\def\bf{\ninebf}%
- \def\it{\nineit}\baselineskip=11pt\rm}%
-
-\font\eightrm=cmr8
-\font\eightbf=cmbx8
-\font\eightit=cmti8
-\font\eighti=cmmi8
-\font\eightsy=cmsy8
-\def\eightpoint{%
- \def\rm{\eightrm}\def\bf{\eightbf}%
- \def\it{\eightit}\def\smc{\eightrm}\baselineskip=10pt\rm%
- \textfont0=\eightrm \scriptfont0=\sixrm
- \textfont1=\eighti \scriptfont1=\sixi
- \textfont2=\eightsy \scriptfont2=\sixsy
- \textfont3=\tenex \scriptfont3=\tenex
-}
-
-\font\sixrm=cmr6
-\font\sixbf=cmbx6
-\font\sixi=cmmi6
-\font\sixsmc=cmr5
-\font\sixsy=cmsy6
-\def\sixpoint{%
- \def\rm{\sixrm}\def\bf{\sixbf}%
- \def\smc{\sixsmc}\baselineskip=8pt\rm}%
-
-\fontdimen13\tensy=2.6pt
-\fontdimen14\tensy=2.6pt
-\fontdimen15\tensy=2.6pt
-\fontdimen16\tensy=1.2pt
-\fontdimen17\tensy=1.2pt
-\fontdimen18\tensy=1.2pt
-
-\font\eightrm=cmr8
-\font\ninerm=cmr9
-\font\twelverm=cmr10 scaled\magstep1
-\font\twelvebf=cmbx10 scaled\magstep 1
-\font\sixteenrm=cmr10 scaled\magstep2
-\def\titlefont{\sixteenrm}
-\def\chapterfont{\twelvebf}
-\def\authorfont{\twelverm}
-\def\rheadfont{\tenrm}
-\def\smc{\tensmc}
-
-
-
-
-%%% COUNTERS FOR HEADINGS %%%
-
-\newcount\headcount
-\headcount=1
-\newcount\seccount
-\seccount=1
-\newcount\subseccount
-\subseccount=1
-\def\reset{\global\seccount=1}
-\global\headcount=0
-
-%%% HEADINGS %%%
-
-\def\headone#1{\global\advance\headcount by 1
-\vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount
-\hskip11truept #1.}\par\nobreak\firstpar\global\advance\headcount by 0
- %\global\advance\seccount by 1
-\reset\vskip2truept}
-
-\def\headtwo#1{%\advance\seccount by -1%
- \vskip12truept\parindent=0pt{\tenpoint\bf\the\headcount.%
- \the\seccount\hskip11truept #1.}\enspace\ignorespaces\firstpar
- \global\advance\headcount by 0\global\advance\seccount by 1}
-% \global\advance\subseccount by 1}
-
-
-%%% THEOREMS, PROOFS, DEFINITIONS, etc. %%%
-
-\def\thm#1{{\smc
-#1\enspace}
-\begingroup\it\ignorespaces\firstpar}
-
-\let\lem=\thm
-\let\cor=\thm
-\let\prop=\thm
-
-\def\endthm{\endgroup}
-\let\endlem=\endthm
-\let\endcor=\endthm
-\let\endprop=\endthm
-
-\def\prf#1{{\it #1.}\rm\enspace\ignorespaces}
-\let\rem=\prf
-\let\case=\prf
-
-
-\def\dfn#1{{\smc
-#1\enspace}
-\rm\ignorespaces}
-
-
-
-%%% FIGURES AND CAPTIONS %%%
-
-\def\caption#1\endcaption{\vskip18pt\ninerm\centerline{#1}\vskip18pt\tenrm}
-
-\newinsert\topins \newif\ifp@ge \newif\if@mid
-\def\topinsert{\@midfalse\p@gefalse\@ins}
-\def\midinsert{\@midtrue\@ins}
-\def\pageinsert{\@midfalse\p@getrue\@ins}
-\skip\topins=0pt %no space added when a topinsert is present
-\count\topins=1000 %magnification factor (1 to 1)
-\dimen\topins=\maxdimen
-\def\@ins{\par\begingroup\setbox0=\vbox\bgroup}
-\def\endinsert{\egroup
- \if@mid \dimen@=\ht0 \advance\dimen@ by\dp0
- \advance\dimen@ by12\p@ \advance\dimen@ by\pagetotal
- \ifdim\dimen@>\pagegoal \@midfalse\p@gefalse\fi\fi
- \if@mid \bigskip \box0 \bigbreak
- \else\insert\topins{\penalty100
- \splittopskip=0pt \splitmaxdepth=\maxdimen \floatingpenalty=0
- \ifp@ge \dimen@=\dp0
- \vbox to\vsize{\unvbox0 \kern-\dimen@}
- \else \box0 \nobreak\bigskip\fi}\fi\endgroup}
-
-
-%%% REFERENCES %%%
-
-\newdimen\refindent@
-\newdimen\refhangindent@
-\newbox\refbox@
-\setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [00]}% Default 2 digits
-\refindent@=\wd\refbox@
-
-\def\resetrefindent#1{%
- \setbox\refbox@=\hbox{\ninepoint\rm\baselineskip=11pt [#1]}%
- \refindent@=\wd\refbox@}
-
-\def\Refs{%
- \unskip\vskip1pc
- \leftline{\noindent\tenpoint\bf References}%
- \penalty10000
- \vskip4pt
- \penalty10000
- \refhangindent@=\refindent@
- \global\advance\refhangindent@ by .5em
- \global\everypar{\hangindent\refhangindent@}%
- \parindent=0pt\ninepoint\rm}
-
-\def\sameauthor{\leavevmode\vbox to 1ex{\vskip 0pt plus 100pt
- \hbox to 2em{\leaders\hrule\hfil}\vskip 0pt plus 300pt}}
-
-\def\ref#1\\#2\endref{\leavevmode\hbox to \refindent@{\hfil[#1]}\enspace #2\par}
-
-
-%%% OUTPUT %%%
-
-\newinsert\margin
-\dimen\margin=\maxdimen
-\count\margin=0 \skip\margin=0pt
-
-
-\def\footnote#1{\edef\@sf{\spacefactor\the\spacefactor}#1\@sf
- \insert\footins\bgroup\eightpoint\hsize=30pc
- \interlinepenalty100 \let\par=\endgraf
- \leftskip=0pt \rightskip=0pt
- \splittopskip=10pt plus 1pt minus 1pt \floatingpenalty=20000
-\smallskip
-\item{#1}\bgroup\strut\aftergroup\@foot\let\next}
-\skip\footins=6pt plus 2pt minus 4pt
-\dimen\footins=30pc
-
-\newif\iftitle
-
-
-\def\titlepage{\global\titletrue\footline={\hss\ninepoint\rm\folio\hss}}
-\def\rhead{\ifodd\pageno CHAPTER TITLE
- \else AUTHORS NAMES\fi}
-
-\def\makefootline{\ifnum\pageno>1\global\footline={\hfill}\fi
- \baselineskip24\p@\vskip12\p@\fullline{\the\footline}}
-\def\leftheadline{\hbox to \pagewidth{
- \vbox to 10pt{}
- {\kern-8pt\tenrm\folio\hfill\ninerm\rhead}}}
-\def\rightheadline{\hbox to \pagewidth{
- \vbox to 10pt{}
- \kern-8pt\ninerm\rhead\hfil
- {\kern-1pc\tenrm\folio}}}
-
-\def\onepageout#1{\shipout\vbox{
-\offinterlineskip
- \vbox to 2.25pc{%
- \iftitle \global\titlefalse
-% \setcornerrules
- \else\ifodd\pageno\rightheadline\else\leftheadline\fi\fi \vfill}
-\vbox to \pageheight{
- \ifvoid\margin\else
- \rlap{\kern31pc\vbox to0pt{\kern4pt\box\margin \vss}}\fi
- #1 %
-\ifvoid\footins\else
- \vskip\skip\footins \kern 0pt
- \hrule height\ruleht width 2.5pc \kern-\ruleht \kern 0pt
- \unvbox\footins\fi
-\boxmaxdepth=\maxdepth}}
-\advancepageno}
-
-\def\setcornerrules{\hbox to \pagewidth{
- \vrule width 1pc height\ruleht \hfil \vrule width 1pc}
- \hbox to \pagewidth{\llap{\sevenrm(page \folio)\kern1pc}
- \vrule height1pc width\ruleht depth0pt
- \hfil \vrule width\ruleht depth0pt}}
-\output{\onepageout{\unvbox255}}
-
-\newbox\partialpage
-\def\begindoublecolumns{\begingroup
- \output={\global\setbox\partialpage=\vbox{\unvbox255\bigskip}}\eject
- \output={\doublecolumnout} \hsize=20pc \vsize=101pc}
-\def\enddoublecolumns{\output={\balancecolumns}\eject
- \endgroup \pagegoal=\vsize}
-
-\def\doublecolumnout{\splittopskip=\topskip \splitmaxdepth=\maxdepth
- \dimen@=50pc \advance\dimen@ by-\ht\partialpage
- \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@
- \onepageout\pagesofar \unvbox255 \penalty\outputpenalty}
-\def\pagesofar{\unvbox\partialpage
- \wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}}
-\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0
- \advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip
- \divide\dimen@ by2 \splittopskip=\topskip
-{\vbadness=10000 \loop \global\setbox3=\copy0
- \global\setbox1=\vsplit3 to\dimen@
- \ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat}
- \setbox0=\vbox to\dimen@{\unvbox1} \setbox2=\vbox to\dimen@{\unvbox 3}
-\pagesofar}
-
-
-
-
-% Turn off @ as being a letter.
-%
-\catcode`\@=13
-
-% End of ptexpprt.sty
-
-
-CUT HERE............