--- manual/s_phys_pkgs/text/exch2.tex	2004/02/11 20:48:14	1.7
+++ manual/s_phys_pkgs/text/exch2.tex	2004/02/17 21:58:56	1.8
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.7 2004/02/11 20:48:14 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.8 2004/02/17 21:58:56 edhill Exp $
 % $Name:  $
 
 %%  * Introduction
@@ -10,151 +10,159 @@
 %%    o automatically inserted at \section{Reference} 
 
 
-\section{exch2: Extended Cubed Sphere Exchange}
+\section{Extended Cubed Sphere Exchange}
 \label{sec:exch2}
 
 
 \subsection{Introduction}
 
-The exch2 package is an extension to the original cubed sphere exchanges
-to allow more flexible domain decomposition and parallelization.  Cube faces
-(subdomains) may be divided into whatever number of tiles that divide evenly
-into the grid point dimensions of the subdomain.  Furthermore, the individual
-tiles may be run on separate processors in different combinations,
-and whether exchanges between particular tiles occur between different
-processors is determined at runtime.
-
-The exchange parameters are declared in {\em W2\_EXCH2\_TOPOLOGY.h} and 
-assigned in {\em w2\_e2setup.F}, both in the 
-{\em pkg/exch2} directory.  The validity of the cube topology depends
-on the {\em SIZE.h} file as detailed below.  Both files are generated by 
-Matlab scripts and
-should not be edited.  The default files provided in the release set up
-a cube sphere arrangement of six tiles, one per subdomain, each with 32x32 grid
-points, running on a single processor.  
+The \texttt{exch2} package is an extension to the original cubed
+sphere exchanges to allow more flexible domain decomposition and
+parallelization.  Cube faces (subdomains) may be divided into whatever
+number of tiles that divide evenly into the grid point dimensions of
+the subdomain.  Furthermore, the individual tiles may be run on
+separate processors in different combinations, and whether exchanges
+between particular tiles occur between different processors is
+determined at runtime.
+
+The exchange parameters are declared in
+\filelink{pkg/exch2/W2\_EXCH2\_TOPOLOGY.h}{pkg-exch2-W2_EXCH2_TOPOLOGY.h}
+and assigned in
+\filelink{pkg/exch2/w2\_e2setup.F}{pkg-exch2-w2_e2setup.F}, both in
+the \texttt{pkg/exch2} directory.  The validity of the cube topology
+depends on the \texttt{SIZE.h} file as detailed below.  Both files are
+generated by Matlab scripts and should not be edited.  The default
+files provided in the release set up a cube sphere arrangement of six
+tiles, one per subdomain, each with 32x32 grid points, running on a
+single processor.
 
 \subsection{Key Variables}
 
 The descriptions of the variables are divided up into scalars,
-one-dimensional arrays indexed to the tile number, and two and three 
-dimensional
-arrays indexed to tile number and neighboring tile.  This division
-actually reflects  the functionality of these variables: the scalars
-are common to every part of the topology, the tile-indexed arrays to 
-individual tiles, and the arrays indexed to tile and neighbor to 
-relationships between tiles and their neighbors.
+one-dimensional arrays indexed to the tile number, and two and three
+dimensional arrays indexed to tile number and neighboring tile.  This
+division actually reflects the functionality of these variables: the
+scalars are common to every part of the topology, the tile-indexed
+arrays to individual tiles, and the arrays indexed to tile and
+neighbor to relationships between tiles and their neighbors.
 
 \subsubsection{Scalars}
 
 The number of tiles in a particular topology is set with the parameter
-{\em NTILES}, and the maximum number of neighbors of any tiles by 
-{\em MAX\_NEIGHBOURS}.  These parameters are used for defining the size of
-the various one and two dimensional arrays that store tile parameters
-indexed to the tile number.
-
-The scalar parameters {\em exch2\_domain\_nxt} and 
-{\em exch2\_domain\_nyt} express the number of tiles in the x and y global
-indices.  For example, the default setup of six tiles has 
-{\em exch2\_domain\_nxt=6} and {\em exch2\_domain\_nyt=1}.  A topology of
-twenty-four square (in gridpoints) tiles, four (2x2) per subdomain, will
-have {\em exch2\_domain\_nxt=12} and {\em 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 {\em 1,bi} (in the
-x axis) and y-axis variable {\em bj} is generally ignored within the package.
+\texttt{NTILES}, and the maximum number of neighbors of any tiles by
+\texttt{MAX\_NEIGHBOURS}.  These parameters are used for defining the
+size of the various one and two dimensional arrays that store tile
+parameters indexed to the tile number.
+
+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 has \texttt{exch2\_domain\_nxt=6} and
+\texttt{exch2\_domain\_nyt=1}.  A topology of twenty-four square (in
+gridpoints) tiles, four (2x2) per subdomain, will have
+\texttt{exch2\_domain\_nxt=12} and \texttt{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 \texttt{1,bi} (in the x axis) and y-axis variable
+\texttt{bj} is generally ignored within the package.
 
 \subsubsection{Arrays Indexed to Tile Number}
 
-The following arrays are of size {\em NTILES}, are indexed to the tile number, 
-and the indices are omitted in their descriptions.
+The following arrays are of size \texttt{NTILES}, are indexed to the
+tile number, and the indices are omitted in their descriptions.
 
-The arrays {\em exch2\_tnx} and {\em exch2\_tny} 
-express the x and y dimensions of each tile.  At present for each tile
-{\em exch2\_tnx = sNx} 
-and {\em exch2\_tny = sNy}, as assigned in {\em SIZE.h}.  Future releases of 
-MITgcm are to allow varying tile sizes.
-
-The location of the tiles' Cartesian origin within a subdomain are determined 
-by the arrays {\em exch2\_tbasex} and {\em exch2\_tbasey}.  These variables
-are used to relate the location of the edges of the tiles to each other.  As 
-an example, in the default six-tile topology (the degenerate case) 
-each index in these arrays are 
-set to 0.  The twenty-four, 32x32 cube face case discussed above will have
-values of 0 or 16, depending on the quadrant the tile falls within the 
-subdomain.  {\em exch2\_myFace} contains the number of the 
-cubeface/subdomain of each tile, numbered 1-6 in the case of the standard
-cube topology.  
-
-The arrays {\em exch2\_txglobalo} and {\em exch2\_txglobalo} are similar to
-{\em exch2\_tbasex} and {\em exch2\_tbasey}, but locate the tiles within
-the global address space, similar to that used by global files.  
-
-The arrays {\em exch2\_isWedge}, {\em exch2\_isEedge}, {\em exch2\_isSedge}, 
-and {\em exch2\_isNedge} are set to 1 if the indexed tile lies on the edge
-of a subdomain, 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 indicates 
-special exchange and numerical handling for the singularities at the eight 
-corners of the cube.  {\em exch2\_isNedge} contains a count of how many
-neighboring tiles each tile has, and is used for setting bounds for looping
-over neighboring tiles.  {\em exch2\_tProc} holds the process rank of each tile,
-and is used in interprocess communication.
+The arrays \varlink{exch2\_tnx}{exch2_tnx} and
+\varlink{exch2\_tny}{exch2_tny} express the x and y dimensions of each
+tile.  At present for each tile \texttt{exch2\_tnx=sNx} and
+\texttt{exch2\_tny=sNy}, as assigned in \texttt{SIZE.h}.  Future
+releases of MITgcm are to allow varying tile sizes.
+
+The location of the tiles' Cartesian origin within a subdomain are
+determined by the arrays \varlink{exch2\_tbasex}{exch2_tbasex} and
+\varlink{exch2\_tbasey}{exch2_tbasey}.  These variables are used to
+relate the location of the edges of the tiles to each other.  As an
+example, in the default six-tile topology (the degenerate case) each
+index in these arrays are set to 0.  The twenty-four, 32x32 cube face
+case discussed above will have values of 0 or 16, depending on the
+quadrant the tile falls within the subdomain.  The array 
+\varlink{exch2\_myFace}{exch2_myFace} contains the number of the
+cubeface/subdomain of each tile, numbered 1-6 in the case of the
+standard cube topology.
+
+The arrays \varlink{exch2\_txglobalo}{exch2_txglobalo} and
+\varlink{exch2\_txglobalo}{exch2_txglobalo} are similar to
+\varlink{exch2\_tbasex}{exch2_tbasex} and
+\varlink{exch2\_tbasey}{exch2_tbasey}, but locate the tiles within the
+global address space, similar to that used by global files.
+
+The arrays \varlink{exch2\_isWedge}{exch2_isWedge},
+\varlink{exch2\_isEedge}{exch2_isEedge},
+\varlink{exch2\_isSedge}{exch2_isSedge}, and
+\varlink{exch2\_isNedge}{exch2_isNedge} are set to 1 if the indexed
+tile lies on the edge of a subdomain, 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 indicates special exchange and numerical
+handling for the singularities at the eight corners of the cube.
+\varlink{exch2\_nNeighbours}{exch2_nNeighbours} contains a count of
+how many 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.
 
 \subsubsection{Arrays Indexed to Tile Number and Neighbor}
 
-The following arrays are all of size {\em MAX\_NEIGHBOURS}x{\em NTILES} and
-describe the orientations between the the tiles.
+The following arrays are all of size \texttt{MAX\_NEIGHBOURS} $\times$
+\texttt{NTILES} and describe the orientations between the the tiles.
 
-The array {\em exch2\_neighbourId(a,T)} holds the tile number $T_{n}$ for each tile 
-{\em T}'s neighbor tile {\em a}.  The neighbor tiles are indexed {\em 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?  
-
-{\em exch2\_opposingSend\_record(a,T)} holds 
-the index c in {\em exch2\_neighbourId(b,$T_{n}$)} that holds the tile number T.
-In other words,
-
-\begin{verbatim}   
-exch2_neighbourId( exch2_opposingSend_record(a,T), 
-                           exch2_neighbourId(a,T) ) = T
+The array \texttt{exch2\_neighbourId(a,T)} holds the tile number for
+each of the $n$ neighboring tiles.  The neighbor tiles are indexed
+\texttt{(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?
+
+The \texttt{exch2\_opposingSend\_record(a,T)} array holds the index c
+in \texttt{exch2\_neighbourId(b,$T_{n}$)} that holds the tile number T.
+In other words, 
+\begin{verbatim}
+   exch2_neighbourId( exch2_opposingSend_record(a,T),
+                      exch2_neighbourId(a,T) ) = T
 \end{verbatim}
+and this provides a back-reference from the neighbor tiles.
 
-% {\em exch2\_neighbourId(exch2\_opposingSend\_record(a,T),exch2\_neighbourId(a,T))=T}.
-% alternate version
-
-This is to provide a backreference from the neighbor tiles.
-
-The arrays {\em exch2\_pi }, {\em exch2\_pj }, {\em exch2\_oi }, 
-{\em exch2\_oj }, {\em exch2\_oi\_f }, and {\em exch2\_oj\_f }  specify 
-the transformations in exchanges between the neighboring tiles.  The dimensions  
-of {\em exch2\_pi(t,N,T) } and {\em exch2\_pj(t,N,T) } are the neighbor ID 
-{ \em N } and the tile number {\em T } as explained above, plus the transformation
-vector {\em t }, of length two.  The first element of the transformation vector indicates
-the factor by which variables representing the same vector component  of a tile 
-will be multiplied, and the second element indicates the transform to the 
-variable in the other direction.  As an example, {\em exch2\_pi(1,N,T) } holds the 
-transform of the i-component of a vector variable in tile {\em T } to the i-component of 
-tile  {\em T }'s neighbor  {\em N }, and {\em exch2\_pi(2,N,T) } hold the component 
-of neighbor  {\em N }'s j-component.
-
-Under the current cube topology, one of the two elements of {\em exch2\_pi } or {\em exch2\_pj }
-for a given tile   {\em T } and  neighbor  {\em N } will be 0, reflecting the fact that
-the vector components are orthogonal.  The other element will be 1 or -1, depending on whether
-the components are indexed in the same or opposite directions.  For example, the transform dimension
-of the arrays for all tile neighbors on the same subdomain will be {\em [1 , 0] }, since all tiles on 
-the same subdomain are oriented identically.  Vectors that correspond to the orthogonal dimension with the 
-same index direction will have {\em [0 , 1] }, whereas those in the opposite index direction will have
-{\em [0 , -1] }.
-
-
+The arrays \varlink{exch2\_pi}{exch2_pi},
+\varlink{exch2\_pj}{exch2_pj}, \varlink{exch2\_oi}{exch2_oi},
+\varlink{exch2\_oj}{exch2_oj}, \varlink{exch2\_oi\_f}{exch2_oi_f}, and
+\varlink{exch2\_oj\_f}{exch2_oj_f} specify the transformations in
+exchanges between the neighboring tiles.  The dimensions of
+\texttt{exch2\_pi(t,N,T)} and \texttt{exch2\_pj(t,N,T)} are the
+neighbor ID \textit{N} and the tile number \textit{T} as explained
+above, plus the transformation vector {\em t }, of length two.  The
+first element of the transformation vector indicates the factor by
+which variables representing the same vector component of a tile will
+be multiplied, and the second element indicates the transform to the
+variable in the other direction.  As an example,
+\texttt{exch2\_pi(1,N,T)} holds the transform of the i-component of a
+vector variable in tile \texttt{T} to the i-component of tile
+\texttt{T}'s neighbor \texttt{N}, and \texttt{exch2\_pi(2,N,T)} hold
+the component of neighbor \texttt{N}'s j-component.
+
+Under the current cube topology, one of the two elements of
+\texttt{exch2\_pi} or \texttt{exch2\_pj} for a given tile \texttt{T}
+and neighbor \texttt{N} will be 0, reflecting the fact that the vector
+components are orthogonal.  The other element will be 1 or -1,
+depending on whether the components are indexed in the same or
+opposite directions.  For example, the transform dimension of the
+arrays for all tile neighbors on the same subdomain will be [1,0],
+since all tiles on the same subdomain are oriented identically.
+Vectors that correspond to the orthogonal dimension with the same
+index direction will have [0,1], whereas those in the opposite index
+direction will have [0,-1].
 
 
-//
-
+{\footnotesize
 \begin{verbatim}
-
-
-
 C      exch2_pi          :: X index row of target to source permutation 
 C                        :: matrix for each neighbour entry.            
 C      exch2_pj          :: Y index row of target to source permutation 
@@ -172,7 +180,7 @@
 C                        :: offset vector for face quantities           
 C                        :: of each neighbor entry.                     
 \end{verbatim}
-
+}