--- manual/s_phys_pkgs/text/exch2.tex	2004/03/17 21:44:02	1.14
+++ manual/s_phys_pkgs/text/exch2.tex	2004/03/18 14:56:25	1.15
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.14 2004/03/17 21:44:02 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.15 2004/03/18 14:56:25 afe Exp $
 % $Name:  $
 
 %%  * Introduction
@@ -281,20 +281,22 @@
 The scalar parameters \varlink{exch2\_domain\_nxt}{exch2_domain_nxt}
 and \varlink{exch2\_domain\_nyt}{exch2_domain_nyt} express the number
 of tiles in the $x$ and $y$ global indices.  For example, the default
-setup of six tiles (Fig. \ref{fig:6tile}) has \code{exch2\_domain\_nxt=6} and
-\code{exch2\_domain\_nyt=1}.  A topology of twenty-four square tiles,
-four per subdomain (as in figure \ref{fig:24tile}), will have
-\code{exch2\_domain\_nxt=12} and \code{exch2\_domain\_nyt=2}.  Note
-that these parameters express the tile layout to allow global data
-files that are tile-layout-neutral and have no bearing on the internal
-storage of the arrays.  The tiles are internally stored in a range
-from \code{(1:\varlink{bi}{bi})} the $x$ axis, and $y$ axis variable
-\varlink{bj}{bj} is generally ignored within the package. \\
+setup of six tiles (Fig. \ref{fig:6tile}) has
+\code{exch2\_domain\_nxt=6} and \code{exch2\_domain\_nyt=1}.  A
+topology of twenty-four square tiles, four per subdomain (as in figure
+\ref{fig:24tile}), will have \code{exch2\_domain\_nxt=12} and
+\code{exch2\_domain\_nyt=2}.  Note that these parameters express the
+tile layout to allow global data files that are tile-layout-neutral
+and have no bearing on the internal storage of the arrays.  The tiles
+are internally stored in a range from \code{(1:\varlink{bi}{bi})} the
+$x$ axis, and the $y$ axis variable \varlink{bj}{bj} is generally
+ignored within the package. \\
 
 \subsubsection{Arrays Indexed to Tile Number}
 
-The following arrays are of length \code{NTILES}, are indexed to the
-tile number, and the indices are omitted in their descriptions. \\
+The following arrays are of length \code{NTILES}and are indexed to the
+tile number, which is indicated in the diagrams with the notation
+\textsf{t}$n$.  The indices are omitted in the descriptions. \\
 
 The arrays \varlink{exch2\_tnx}{exch2_tnx} and
 \varlink{exch2\_tny}{exch2_tny} express the $x$ and $y$ dimensions of
@@ -324,7 +326,7 @@
 standard cube topology and indicated by \textbf{\textsf{f}}$n$ in
 figures \ref{fig:12tile} and
 \ref{fig:24tile}. \varlink{exch2\_nNeighbours}{exch2_nNeighbours}
-contains a count of how many neighboring tiles each tile has, and is
+contains a count the  neighboring tiles each tile has, and is
 used for setting bounds for looping over neighboring tiles.
 \varlink{exch2\_tProc}{exch2_tProc} holds the process rank of each
 tile, and is used in interprocess communication.  \\
@@ -334,10 +336,10 @@
 \varlink{exch2\_isEedge}{exch2_isEedge},
 \varlink{exch2\_isSedge}{exch2_isSedge}, and
 \varlink{exch2\_isNedge}{exch2_isNedge} are set to \code{1} if the
-indexed tile lies on the edge of a subdomain, \code{0} if not.  The
-values are used within the topology generator to determine the
-orientation of neighboring tiles, and to indicate whether a tile lies
-on the corner of a subdomain.  The latter case requires special
+indexed tile lies on the respective edge of a subdomain, \code{0} if
+not.  The values are used within the topology generator to determine
+the orientation of neighboring tiles, and to indicate whether a tile
+lies on the corner of a subdomain.  The latter case requires special
 exchange and numerical handling for the singularities at the eight
 corners of the cube. \\
 
@@ -350,15 +352,15 @@
 
 The array \code{exch2\_neighbourId(a,T)} holds the tile number
 \code{Tn} for each of the tile number \code{T}'s neighboring tiles
-\code{a}.  The neighbor tiles are indexed \code{(1:MAX\_NEIGHBOURS)}
-in the order right to left on the north then south edges, and then top
-to bottom on the east and west edges.  Maybe throw in a fig here, eh?
-\\
-
-\sloppy
-The \code{exch2\_opposingSend\_record(a,T)} array holds the index
-\code{b} in \texttt{exch2\_neighbourId(b,Tn)} that holds the tile
-number \code{T}.  In other words,
+\code{a}.  The neighbor tiles are indexed
+\code{(1:exch2\_NNeighbours(T))} in the order right to left on the
+north then south edges, and then top to bottom on the east and west
+edges.  Maybe throw in a fig here, eh?  \\
+
+\sloppy The \code{exch2\_opposingSend\_record(a,T)} array holds the
+index \code{b} of the element in \texttt{exch2\_neighbourId(b,Tn)}
+that holds the tile number \code{T}, given
+\code{Tn=exch2\_neighborId(a,T)}.  In other words,
 \begin{verbatim}
    exch2_neighbourId( exch2_opposingSend_record(a,T),
                       exch2_neighbourId(a,T) ) = T
@@ -366,40 +368,35 @@
 This provides a back-reference from the neighbor tiles. \\
 
 The arrays \varlink{exch2\_pi}{exch2_pi} and
-\varlink{exch2\_pj}{exch2_pj} specify the transformations of variables
+\varlink{exch2\_pj}{exch2_pj} specify the transformations of indices
 in exchanges between the neighboring tiles.  These transformations are
-necessary in exchanges between subdomains because a physical vector
-component in one direction may map to one in a different direction in
-an adjacent subdomain, and may be have its indexing reversed. This
-swapping arises from the ``folding'' of two-dimensional arrays into a
-three-dimensional cube.
+necessary in exchanges between subdomains because the array index in
+one dimension may map to the other index in an adjacent subdomain, and
+may be have its indexing reversed. This swapping arises from the
+``folding'' of two-dimensional arrays into a three-dimensional cube.
 
 The dimensions of \code{exch2\_pi(t,N,T)} and \code{exch2\_pj(t,N,T)}
 are the neighbor ID \code{N} and the tile number \code{T} as explained
-above, plus a vector of length 2 containing transformation factors
-\code{t}.  The first element of the transformation vector indicates
-the factor \code{t} by which variables representing the same
-\emph{physical} vector component of a tile \code{T} will be multiplied
-in exchanges with neighbor \code{N}, and the second element indicates
-the transform to the physical vector in the other direction.  To
-clarify (hopefully), \code{exch2\_pi(1,N,T)} holds the transform of
-the $i$ component of a vector variable in tile \code{T} to the $i$
-component of tile \code{T}'s neighbor \code{N}, and
-\code{exch2\_pi(2,N,T)} holds the transform of \code{T}'s $i$
-components to the neighbor \code{N}'s $j$ component. \\
+above, plus a vector of length \code{2} containing transformation
+factors \code{t}.  The first element of the transformation vector
+holds the factor to multiply the index in the same axis, and the
+second element holds the the same for the orthogonal index.  To
+clarify, \code{exch2\_pi(1,N,T)} holds the mapping of the $x$ axis
+index of tile \code{T} to the $x$ axis of tile \code{T}'s neighbor
+\code{N}, and \code{exch2\_pi(2,N,T)} holds the mapping of \code{T}'s
+$x$ index to the neighbor \code{N}'s $y$ index. \\
  
-Under the current cube topology, one of the two elements of
-\code{exch2\_pi} or \code{exch2\_pj} for a given tile \code{T} and
-neighbor \code{N} will be \code{0}, reflecting the fact that the two
-vector components are orthogonal.  The other element will be \code{1}
-or \code{-1}, depending on whether the components are indexed in the
-same or opposite directions.  For example, the transform vector of the
-arrays for all tile neighbors on the same subdomain will be
+One of the two elements of \code{exch2\_pi} or \code{exch2\_pj} for a
+given tile \code{T} and neighbor \code{N} will be \code{0}, reflecting
+the fact that the two axes are orthogonal.  The other element will be
+\code{1} or \code{-1}, depending on whether the axes are indexed in
+the same or opposite directions.  For example, the transform vector of
+the arrays for all tile neighbors on the same subdomain will be
 \code{(1,0)}, since all tiles on the same subdomain are oriented
-identically.  A vector direction that corresponds to the orthogonal
-dimension with the same index direction in a particular tile-neighbor
-orientation will have \code{(0,1)}, whereas those in the opposite
-index direction will have \code{(0,-1)}. \\
+identically.  An axis that corresponds to the orthogonal dimension
+with the same index direction in a particular tile-neighbor
+orientation will have \code{(0,1)}.  Those in the opposite index
+direction will have \code{(0,-1)} in order to reverse the ordering. \\
 
 The arrays \varlink{exch2\_oi}{exch2_oi},
 \varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and
