--- manual/s_phys_pkgs/text/exch2.tex	2004/01/28 18:08:22	1.2
+++ manual/s_phys_pkgs/text/exch2.tex	2004/03/15 22:39:28	1.11
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.2 2004/01/28 18:08:22 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/exch2.tex,v 1.11 2004/03/15 22:39:28 afe Exp $
 % $Name:  $
 
 %%  * Introduction
@@ -10,21 +10,305 @@
 %%    o automatically inserted at \section{Reference} 
 
 
-\section{exch2: Extended Cubed Sphere Exchange}
-
-\subsection{Introduction}
-
-The exch2 package is an extension to the original cubed sphere exchanges
-to allow more flexible domain decomposition and parallelization.  Cube faces
-(subdomain) 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 different processors in any combination, (tone this down 
-a bit), and whether exchanges between particular tiles occur between different
-processors is decided at runtime.
-
+\section{exch2: Extended Cubed Sphere \mbox{Topology}}
+\label{sec:exch2}
 
 
+\subsection{Introduction}
 
+The \texttt{exch2} package is an extension to the original cubed
+sphere topological configuration that allows more flexible domain
+decomposition and parallelization.  Cube faces (also called
+subdomains) may be divided into any 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.  This
+flexibility provides for manual compile-time load balancing across a
+relatively arbitrary number of processors. \\
+
+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}. The
+validity of the cube topology depends on the \file{SIZE.h} file as
+detailed below.  Both files are generated by Matlab scripts in
+\file{utils/exch2/matlab-topology-generator}; see Section
+\ref{sec:topogen} \sectiontitle{Generating Topology Files for exch2}
+for details on creating alternate topologies.  The default files
+provided in the release configure a cubed sphere topology of six
+tiles, one per subdomain, each with 32$\times$32 grid points, all
+running on a single processor.  Pregenerated examples of these files
+with alternate topologies are provided under
+\file{utils/exch2/code-mods} along with the appropriate \file{SIZE.h}
+file for single-processor execution.
+
+\subsection{Invoking exch2}
+
+To use exch2 with the cubed sphere, the following conditions must be
+met: \\
+
+$\bullet$ The exch2 package is included when \file{genmake2} is run.
+  The easiest way to do this is to add the line \code{exch2} to the
+  \file{profile.conf} file -- see Section
+  \ref{sect:buildingCode}\sectiontitle{Building the code} for general
+  details. \\
+
+$\bullet$ An example of \file{W2\_EXCH2\_TOPOLOGY.h} and
+  \file{w2\_e2setup.F} must reside in a directory containing code
+  linked when \file{genmake2} runs.  The safest place to put these
+  is the directory indicated in the \code{-mods=DIR} command line
+  modifier (typically \file{../code}), or the build directory.  The
+  default versions of these files reside in \file{pkg/exch2} and are
+  linked automatically if no other versions exist elsewhere in the
+  link path, but they should be left untouched to avoid breaking
+  configurations other than the one you intend to modify.\\
+
+$\bullet$ Files containing grid parameters, named
+  \file{tile???.mitgrid} where \file{???} is \file{001} through
+  \file{006} (one per subdomain), must be in the working directory
+  when the MITgcm executable is run.  These files are provided in the
+  example experiments for cubed sphere configurations with
+  32$\times$32 cube sides and are non-trivial to generate -- please
+  contact MITgcm support if you want to generate files for other
+  configurations. \\
+
+$\bullet$ As always when compiling MITgcm, the file \file{SIZE.h}
+  must be placed where \file{genmake2} will find it.  In particular
+  for the exch2, the domain decomposition specified in \file{SIZE.h}
+  must correspond with the particular configuration's topology
+  specified in \file{W2\_EXCH2\_TOPOLOGY.h} and
+  \file{w2\_e2setup.F}.  Domain decomposition issues particular to
+  exch2 are addressed in Section \ref{sec:topogen} \sectiontitle{Generating
+  Topology Files for exch2}; a more general background on the subject
+  relvant to MITgcm is presented in Section
+  \ref{sect:specifying_a_decomposition}\sectiontitle{Specifying a
+  decomposition}.\\
+
+As of the time of writing the following examples use exch2 and may be
+used for guidance:
+
+\begin{verbatim}
+verification/adjust_nlfs.cs-32x32x1
+verification/adjustment.cs-32x32x1 
+verification/aim.5l_cs
+verification/global_ocean.cs32x15
+verification/hs94.cs-32x32x5
+\end{verbatim}
+
+
+
+
+\subsection{Generating Topology Files for exch2}
+\label{sec:topogen}
+
+Alternate cubed sphere topologies may be created using the Matlab
+scripts in \file{utils/exch2/matlab-topology-generator}. Running the
+m-file \file{driver.m} from the Matlab prompt (there are no parameters
+to pass) generates exch2 topology files \file{W2\_EXCH2\_TOPOLOGY.h}
+and \file{w2\_e2setup.F} in the working directory and displays a
+figure of the topology via Matlab.  The other m-files in the directory
+are subroutines of \file{driver.m} and should not be run except for
+development purposes. \\
+
+The parameters that determine the dimensions and topology of the
+generated configuration are \code{nr}, \code{nb}, \code{ng},
+\code{tnx} and \code{tny}, and all are assigned early in the script.
+
+The first three determine the size of the subdomains (cube faces) and
+hence the size of the overall domain.  Each one determines the number
+of grid points, and therefore the resolution, along the subdomain
+sides in a ``great circle'' around each axis of the cube.  At the time
+of this writing MITgcm requires these three parameters to be equal,
+but they provide for future releases of MITgcm to accomodate different
+resolutions around the axes to allow (for example) greater resolution
+around the equator.\\
+
+The parameters \code{tnx} and \code{tny} determine the dimensions of
+the tiles into which the subdomains are decomposed, and must evenly
+divide the integer assigned to \code{nr}, \code{nb} and \code{ng}.
+The result is a rectangular tiling of the subdomain.  Figure
+\ref{fig:24tile} shows one possible topology for a twenty-four tile
+cube, and figure \ref{fig:12tile} shows one for twelve tiles. \\
+
+\begin{figure}
+\begin{center}
+ \resizebox{4in}{!}{
+  \includegraphics{part6/s24t_16x16.ps}
+ }
+\end{center} 
+\caption{Plot of cubed sphere topology with a 32$\times$32 grid and
+twenty-four tiles (\code{tnx=16, tny=16})
+} \label{fig:24tile}
+\end{figure}
+
+\begin{figure}
+\begin{center}
+ \resizebox{4in}{!}{
+  \includegraphics{part6/s12t_16x32.ps}
+ }
+\end{center} 
+\caption{Plot of cubed sphere topology with a 32$\times$32 grid and
+twelve tiles (\code{tnx=16, tny=32})
+} \label{fig:12tile}
+\end{figure}
+
+Tiles can be selected from the topology to be omitted from being
+allocated memory and processors.  This kind otuning is useful in
+ocean modeling for omitting tiles that fall entirely on land.  The
+tiles omitted are specified in the file \file{blanklist.txt} by
+their tile number in the topology, separated by a newline. \\
+
+
+
+
+
+
+\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.
+
+\subsubsection{Scalars}
+
+The number of tiles in a particular topology is set with the parameter
+\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 \texttt{NTILES}, are indexed to the
+tile number, and the indices are omitted in their descriptions.
+
+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 \texttt{MAX\_NEIGHBOURS} $\times$
+\texttt{NTILES} and describe the orientations between the the tiles.
+
+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.
+
+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 
+C                        :: matrix for each neighbour entry.            
+C      exch2_oi          :: X index element of target to source 
+C                        :: offset vector for cell-centered quantities  
+C                        :: of each neighbor entry.                     
+C      exch2_oj          :: Y index element of target to source 
+C                        :: offset vector for cell-centered quantities  
+C                        :: of each neighbor entry.                     
+C      exch2_oi_f        :: X index element of target to source 
+C                        :: offset vector for face quantities           
+C                        :: of each neighbor entry.                     
+C      exch2_oj_f        :: Y index element of target to source 
+C                        :: offset vector for face quantities           
+C                        :: of each neighbor entry.                     
+\end{verbatim}
+}