\chapter{The MPI Wrapper Object and Driver}
\label{section:MPI}
\par
The goal is to solve $AX = Y$ in a distributed environment using MPI.
Section 9 of the User's Manual presents a listing of the 
{\tt AllInOneMPI} driver program for solving $AX =Y$.
There are thirteen steps, and each requires ``mid-level'' knowledge 
of several objects of the {\bf SPOOLES} library.
To reduce the complexity of using the library, 
we created the {\tt BridgeMPI} object.
The term ``bridge'' symbolizes spanning the distance between the
{\bf SPOOLES} library and the CSAR Nastran application code.
The ten steps of the {\tt allInOneMPI} driver program is reduced to
five using the {\tt BridgeMPI} object.
\begin{itemize}
\item Initialization and setup step.
\par
Here the {\tt BridgeMPI} object is allocated via a call to 
{\tt BridgeMPI\_new()}.
Parameters are set using {\tt BridgeMPI\_set*()} methods.
The setup phase orders the matrix and prepares all the necessary 
{\bf SPOOLES} data structures for the factorization and solve 
that follows.
\item Setup the numerical factorization.
\par
In this step, 
{\tt BridgeMPI\_factorSetup()} is called
to define the parallelism for the factorization,
and all data structures for the parallel execution are created.
\item Factorization step.
\par
The matrix is factored via a call to {\tt BridgeMPI\_factor()}.
\item Setup the numerical solves.
\par
{\tt BridgeMPI\_solveSetup()} is called to set up the parallel solves.
This must be called {\it once} after a factorization,
one or more solves may follow.
\item Solution step.
\par
The linear system is solved via a call to {\tt BridgeMPI\_solve()}.
\end{itemize}
\par
The {\tt BridgeMPI} object 
has many parameters that control the ordering of the matrix,
the pivoting tolerance (if pivoting is requested),
the drop tolerance (for an approximate factorization),
and so on.
Rather than burden the user with the knowledge of and setting these
parameters, there are decent default values built into the object.
Using the {\tt BridgeMPI} object to solve a linear system of equations 
can be broken down into three steps.
\par
Section~\ref{section:BridgeMPI:quick-look-MPI-driver} takes a quick
look at the {\tt BridgeMPI} driver program (whose complete listing is
found in Appendix~\ref{chapter:MPI_driver}).
Section~\ref{section:BridgeMPI:dataStructure} describes the internal 
data fields of the {\tt BridgeMPI} object.
Section~\ref{section:Bridge:proto} contains the prototypes and
descriptions of all {\tt Bridge} methods.
\par
\section{A quick look at the MPI driver program}
\label{section:BridgeMPI:quick-look-MPI-driver}
\par
The entire listing of this MPI driver is found in
Appendix~\ref{chapter:MPI_driver}.
We now extract parts of the code.
\begin{itemize}
\item Decode the input.
\par
\begin{verbatim}
msglvl       = atoi(argv[1]) ;
msgFileName  = argv[6] ;
neqns        = atoi(argv[3]) ;
type         = atoi(argv[4]) ;
symmetryflag = atoi(argv[5]) ;
mtxFileName  = argv[6] ;
rhsFileName  = argv[7] ;
solFileName  = argv[8] ;
seed         = atoi(argv[9]) ;
\end{verbatim}
Here is a description of the input parameters.

\begin{itemize}
\item {\tt msglvl} is the message level.
\item {\tt msgFile} is the message file name
\item {\tt neqns} is the number of equations.
\item {\tt type} is the type of entries:
1 ({\tt SPOOLES\_REAL}) or
2 ({\tt SPOOLES\_COMPLEX}).
\item {\tt symmetryflag} is the type of matrix symmetry:
0 ({\tt SPOOLES\_SYMMETRIC}),
1 ({\tt SPOOLES\_HERMITIAN}) or
2 ({\tt SPOOLES\_NONSYMMETRIC}).
\item {\tt mtxFile} is the name of the file from which to read the {\tt
InpMtx} object for $A$.
The file name must have the form {\tt *.inpmtxb} for a binary file or
{\tt *.inpmtxf} for a formatted file.
\item {\tt rhsFile} is the name of the file from which to read the {\tt
DenseMtx} object for the right hand side $Y$.
The file name must have the form {\tt *.densemtxb} for a binary file or
{\tt *.densemtxf} for a formatted file.
\item {\tt solFile} is the name of the file to write the {\tt
DenseMtx} object for the solution $X$.
The file name must have the form {\tt *.densemtxb} for a binary file or
{\tt *.densemtxf} for a formatted file, {\tt "none"} for no output,
or any other name for a human-readable listing.
\item {\tt seed} is a random number seed used in the ordering process.
\end{itemize}
%
\item Processor 0 reads in the {\tt InpMtx} object for $A$.
\begin{verbatim}
mtxA = InpMtx_new() ;
rc = InpMtx_readFromFile(mtxA, mtxFileName) ;
\end{verbatim}
The {\tt rc} parameter is the error return. 
Processor 0 then broadcasts the error return to the other processors.
If an error occured reading in the matrix, all processors call
\texttt{MPI\_Finalize()} and exit.
%
\item Processor 0 reads in the {\tt DenseMtx} object for $Y$.
\begin{verbatim}
mtxY = DenseMtx_new() ;
rc = DenseMtx_readFromFile(mtxY, mtxFileName) ;
DenseMtx_dimensions(mtxY, &nrow, &nrhs) ;
\end{verbatim}
The {\tt nrhs} parameter contains the number of right hand sides,
or equivalently, the number of columns in $Y$.
Processor 0 then broadcasts the error return to the other processors.
If an error occured reading in the matrix, all processors call
\texttt{MPI\_Finalize()} and exit.
%
\item Create and setup the {\tt BridgeMPI} object.
\begin{verbatim}
bridge = BridgeMPI_new() ;
BridgeMPI_setMPIparams(bridge, nproc, myid, MPI_COMM_WORLD) ;
BridgeMPI_setMatrixParams(bridge, neqns, type, symmetryflag) ;
BridgeMPI_setMessageInfo(bridge, msglvl, msgFile) ;
rc = BridgeMPI_setup(bridge, mtxA) ;
\end{verbatim}
The {\tt BridgeMPI} object is allocated by {\tt BridgeMPI\_new()},
and various parameters are set.
The actual ordering of the matrix, symbolic factorization,
and permutation creation are performed inside the 
{\tt BridgeMPI\_setup()} method.
%
\item Setup the numerical factorization.
\begin{verbatim}
rc = BridgeMPI_factorSetup(bridge, 0, 0.0) ;
\end{verbatim}
This step tells the \texttt{BridgeMPI} object the number of threads
to be used in the factorization and solve.
The second and third parameters define the particular type 
of map of the computations to processors.
When the second parameter is zero, the defaults map is used.
If {\tt rc = 1}, the setup completed without any error.
%
\item Compute the matrix factorization.
\begin{verbatim}
permuteflag = 1 ;
rc = BridgeMPI_factor(bridge, mtxA, permuteflag, &error) ;
\end{verbatim}
When {\tt permuteflag} is {\tt 1}, it means that the matrix in {\tt
mtxA} has not yet been permuted into the new ordering and so is
done inside the method.
The {\tt error} flag is filled with an error code that tells how far the
factorization was able to proceed.
If {\tt rc = 1}, the factorization completed without any error.
%
\item Setup the solve.
\begin{verbatim}
rc = BridgeMPI_solveSetup(bridge) ;
\end{verbatim}
This method sets up the environment for a parallel solve.
It is called once per factorization, not once per solve.
If {\tt rc = 1}, the setup completed without any error.
%
\item Solve the linear system.
Processor 0 initializes the \texttt{DenseMtx} object {\tt mtxX} to
hold the global solution $X$.
Its entries are explicitly zeroed (this is not necessary but is a good
idea in general).
The solution is then solved.
\begin{verbatim}
mtxX = DenseMtx_new() ;
DenseMtx_init(mtxX, type, 0, 0, neqns, nrhs, 1, neqns) ;
DenseMtx_zero(mtxX) ;
\end{verbatim}
All processors then cooperate to compute the solution $X$.
\begin{verbatim}
rc = BridgeMPI_solve(bridge, permuteflag, mtxX, mtxY) ;
\end{verbatim}
Again, note the presence of {\tt permuteflag}.
When {\tt 1}, \texttt{mtxY} needs to be permuted into the new ordering,
and \texttt{mtxX} is returned in the original ordering.
\end{itemize}
\par
\section{The \texttt{BridgeMPI} Data Structure}
\label{section:BridgeMPI:dataStructure}
\par
The {\tt BridgeMPI} structure has the following fields.
\begin{itemize}
%
\item Graph parameters:
\begin{itemize} 
\item
{\tt int neqns} : number of equations, 
i.e., number of vertices in the graph.
\item
{\tt int nedges} : number of edges 
(includes $(u,v)$, $(v,u)$ and $(u,u)$).
\item
{\tt int Neqns} : number of equations in the compressed graph.
\item
{\tt int Nedges} : number of edges in the compressed graph.
\end{itemize}
%
\item Ordering parameters:
\begin{itemize}
\item
{\tt int maxdomainsize} : maximum size of a subgraph to not split any
further during the nested dissection process.
\item
{\tt int maxnzeros} : maximum number of zeros to allow in a front 
during the supernode amalgamation process.
\item
{\tt int maxsize} : maximum size of a front when the fronts are split.
\item
{\tt int seed} : random number seed.
\item
{\tt double compressCutoff} : if the \texttt{Neqns} $<$
\texttt{compressCutoff} $*$ \texttt{neqns}, then the compressed
graph is formed, ordered and used to create the symbolic
factorization.
\end{itemize}
%
\item Matrix parameters:
\begin{itemize}
\item
{\tt int type} : type of entries,
{\tt SPOOLES\_REAL} or {\tt SPOOLES\_COMPLEX},
default value is {\tt SPOOLES\_REAL}.
\item
{\tt int symmetryflag} : type of symmetry for the matrix,
{\tt SPOOLES\_SYMMETRIC}, {\tt SPOOLES\_HERMITIAN}
or {\tt SPOOLES\_NONSYMMETRIC},
default value is {\tt SPOOLES\_SYMMETRIC}.
\end{itemize}
%
\item Factorization parameters:
\begin{itemize}
\item
{\tt int sparsityflag} : 
{\tt SPOOLES\_DENSE\_FRONTS} for a direct factorization,
or {\tt SPOOLES\_SPARSE\_FRONTS} for an approximate factorization,
default value is {\tt SPOOLES\_DENSE\_FRONTS}.
\item
{\tt int pivotingflag} : 
{\tt SPOOLES\_PIVOTING} for pivoting enabled,
or {\tt SPOOLES\_NO\_PIVOTING} for no pivoting,
default value is {\tt SPOOLES\_NO\_PIVOTING}.
\item
{\tt double tau} : used when pivoting is enabled,
all entries in $L$ and $U$ have magnitude less than or equal to
\texttt{tau},
default value is 100.
\item
{\tt double droptol} : used for an approximation,
all entries in $L$ and $U$ that are kept 
have magnitude greater than or equal to \texttt{droptol}.
default value is 0.001.
\item
{\tt PatchAndGoInfo *patchinfo} : pointer to an object that
controls special factorizations for optimization matrices
and singular matrices from structural analysis,
default value is \texttt{NULL} which means no special action is taken.
See the Reference Manual for more information.
\item
{\tt int lookahead} : this parameter is used to possibly reduce the
idle time of threads during the factorization.
When {\tt lookahead} is 0, the factorization uses the least amount
of working storage but threads can be idle.
Larger values of {\tt lookahead} tend to increase the working
storage but may decrease the execution time.
Values of {\tt lookahead} greater than {\tt nthread} are not useful.
\end{itemize}
%
\item Pointers to objects:
\begin{itemize}
\item
{\tt ETree *frontETree} : object that defines the factorizations,
e.g., the number of fronts, the tree they form, the number of
internal and external rows for each front, and the map from
vertices to the front where it is contained.
\item
{\tt IVL *symbfacIVL} : object that contains the symbolic
factorization of the matrix.
\item
{\tt SubMtxManager *mtxmanager} : object that manages the
\texttt{SubMtx} objects that store the factor entries and are used
in the solves.
\item
{\tt FrontMtx *frontmtx} : object that stores the $L$, $D$ and $U$
factor matrices.
\item
{\tt IV *oldToNewIV} : object that stores old-to-new permutation vector.
\item
{\tt IV *newToOldIV} : object that stores new-to-old permutation vector.
\end{itemize}
%
\item MPI information:
\begin{itemize}
\item
{\tt int nproc} : number of processors.
\item
{\tt int myid} : id of this processor.
\item
{\tt MPI\_Comm} : MPI communicator.
\item
{\tt IV *ownersIV} : this object contains the map from fronts to
their owning processors.
\item
{\tt SolveMap *solvemap} : this object contains the map from factor
submatrices to their owning processors.
\item
{\tt DV *cumopsDV} : this object is formed when the map from
fronts to owning processors is created.
Its size is {\tt nthread} and contains the operations that each
thread will perform during a direct factorization without pivoting.
\item
{\tt IV *vtxmapIV} : this object contains the map from vertices
to their owning processors.
\item
{\tt IV *rowmapIV} : this object contains the map from rows
to their owning processors during the solve. This may be different
from {\tt vtxmapIV} if pivoting is enabled.
\item
{\tt IV *ownedColumnsIV} : this object contains the columns of the
matrix that are owned by this processor during the solve.
\item
{\tt InpMtx *Aloc} : this object contains the entries of $A$ that
are local to this processor during the factorization.
\item
{\tt DenseMtx *Xloc} : this object contains the local solution
during the solve.
\item
{\tt DenseMtx *Yloc} : this object contains the local right hand
side during the solve.
\end{itemize}
%
\item Message information, statistics and cpu times:
\begin{itemize}
\item
{\tt int msglvl} : message level for output.
When 0, no output, When 1, just statistics and cpu times.
When greater than 1, more and more output.
\item
{\tt FILE *msgFile} : message file for output.
When \texttt{msglvl} $>$ 0, \texttt{msgFile} must not be \texttt{NULL}.
\item
{\tt int stats[6]} : statistics for the factorization.
\begin{center}
\begin{tabular}{ll}
\texttt{stats[0]} : & \# of pivots \\
\texttt{stats[1]} : & \# of pivot tests \\
\texttt{stats[2]} : & \# of delayed rows and columns
\end{tabular}
\begin{tabular}{ll}
\texttt{stats[3]} : & \# of entries in $D$ \\
\texttt{stats[4]} : & \# of entries in $L$ \\
\texttt{stats[5]} : & \# of entries in $U$
\end{tabular}
\end{center}
\item
{\tt double cpus[22]} : cpus for the different functions.
\begin{center}
\begin{tabular}{ll}
\texttt{cpus[0]} : & construct \texttt{Graph} \\
\texttt{cpus[1]} : & compress \texttt{Graph} \\
\texttt{cpus[2]} : & order \texttt{Graph} \\
\texttt{cpus[3]} : & symbolic factorization \\
\texttt{cpus[4]} : & broadcast the front tree \\
\texttt{cpus[5]} : & broadcast symbolic factor \\
\texttt{cpus[6]} : & total setup time \\
\texttt{cpus[7]} : & setup the factorization \\
\texttt{cpus[8]} : & permute matrix \\
\texttt{cpus[9]} : & distribute matrix \\
\texttt{cpus[10]} : & initialize front matrix 
\end{tabular}
\begin{tabular}{ll}
\texttt{cpus[11]} : & factor matrix \\
\texttt{cpus[12]} : & post-process matrix \\
\texttt{cpus[13]} : & total factor time \\
\texttt{cpus[14]} : & setup the parallel solve \\
\texttt{cpus[15]} : & permute rhs \\
\texttt{cpus[16]} : & distribute rhs \\
\texttt{cpus[17]} : & create solution matrix \\
\texttt{cpus[18]} : & solve \\
\texttt{cpus[19]} : & gather solution \\
\texttt{cpus[20]} : & permute solution \\
\texttt{cpus[21]} : & total solve time
\end{tabular}
\end{center}
\end{itemize}
\end{itemize}
\par
\section{Prototypes and descriptions of \texttt{BridgeMPI} methods}
\label{section:BridgeMPI:proto}
\par
This section contains brief descriptions including prototypes
of all methods that belong to the {\tt BridgeMPI} object.
\par
\subsection{Basic methods}
\label{subsection:BridgeMPI:proto:basics}
\par
As usual, there are four basic methods to support object creation,
setting default fields, clearing any allocated data, and free'ing
the object.
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
BridgeMPI * BridgeMPI_new ( void ) ;
\end{verbatim}
\index{BridgeMPI_new@{\tt BridgeMPI\_new()}}
This method simply allocates storage for the {\tt BridgeMPI} structure 
and then sets the default fields by a call to 
{\tt BridgeMPI\_setDefaultFields()}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setDefaultFields ( BridgeMPI *bridge ) ;
\end{verbatim}
\index{BridgeMPI_setDefaultFields@{\tt BridgeMPI\_setDefaultFields()}}
The structure's fields are set to default values:
\begin{itemize}
\item
\texttt{neqns} = \texttt{nedges} = \texttt{Neqns} =
\texttt{Nedges} = 0.
\item
\texttt{maxdomainsize} = \texttt{maxnzeros} 
   = \texttt{maxsize} = \texttt{seed} = -1.
\texttt{compressCutoff} = 0.
\item
\texttt{type} = \texttt{SPOOLES\_REAL}.
\item
\texttt{symmetryflag} = \texttt{SPOOLES\_SYMMETRIC}.
\item
\texttt{sparsityflag} = \texttt{SPOOLES\_DENSE\_FRONTS}.
\item
\texttt{pivotingflag} = \texttt{SPOOLES\_NO\_PIVOTING}.
\item
\texttt{tau} = 100., \texttt{droptol} = 0.001.
\item
\texttt{lookahead} = \texttt{nproc} = 0.
\item
\texttt{myid} = -1.
\item
\texttt{patchinfo},
\texttt{frontETree},
\texttt{symbfacIVL},
\texttt{mtxmanager},
\texttt{frontmtx},
\texttt{oldToNewIV},
\texttt{newToOldIV},
\texttt{ownersIV},
\texttt{solvemap},
\texttt{cumopsDV},
\texttt{vtxmapIV},
\texttt{rowmapIV},
\texttt{ownedColumnsIV},
\texttt{Aloc},
\texttt{Xloc},
\texttt{Yloc} and
\texttt{comm}
are all set to \texttt{NULL}.
\end{itemize}
The \texttt{stats[6]} and \texttt{cpus[22]} vectors are filled 
with zeros.
\par \noindent {\it Return value:}
1 for a normal return, -1 if \texttt{bridge} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_clearData ( BridgeMPI *bridge ) ;
\end{verbatim}
\index{BridgeMPI_clearData@{\tt BridgeMPI\_clearData()}}
This method clears the object and free's any owned data.
It then calls {\tt BridgeMPI\_setDefaultFields()}.
\par \noindent {\it Return value:}
1 for a normal return, -1 if \texttt{bridge} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_free ( BridgeMPI *bridge ) ;
\end{verbatim}
\index{BridgeMPI_free@{\tt BridgeMPI\_free()}}
This method releases any storage by a call to
{\tt BridgeMPI\_clearData()} and then free the space for {\tt bridge}.
\par \noindent {\it Return value:}
1 for a normal return, -1 if \texttt{bridge} is \texttt{NULL}.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Instance methods}
\label{subsection:BridgeMPI:proto:instance}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_oldToNewIV ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_oldToNewIV@{\tt BridgeMPI\_oldToNewIV()}}
This method fills \texttt{*pobj} with its \texttt{oldToNewIV} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_newToOldIV ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_newToOldIV@{\tt BridgeMPI\_newToOldIV()}}
This method fills \texttt{*pobj} with its \texttt{newToOldIV} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_frontETree ( BridgeMPI *bridge, ETree **pobj ) ;
\end{verbatim}
\index{BridgeMPI_frontETree@{\tt BridgeMPI\_frontETree()}}
This method fills \texttt{*pobj} with its \texttt{frontETree} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_symbfacIVL ( BridgeMPI *bridge, IVL **pobj ) ;
\end{verbatim}
\index{BridgeMPI_symbfacIVL@{\tt BridgeMPI\_symbfacIVL()}}
This method fills \texttt{*pobj} with its \texttt{symbfacIVL} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_mtxmanager ( BridgeMPI *bridge, SubMtxManager **pobj ) ;
\end{verbatim}
\index{BridgeMPI_mtxmanager@{\tt BridgeMPI\_mtxmanager()}}
This method fills \texttt{*pobj} with its \texttt{mtxmanager} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_frontmtx ( BridgeMPI *bridge, FrontMtx **pobj ) ;
\end{verbatim}
\index{BridgeMPI_frontmtx@{\tt BridgeMPI\_frontmtx()}}
This method fills \texttt{*pobj} with its \texttt{frontmtx} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_ownersIV ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_ownersIV@{\tt BridgeMPI\_ownersIV()}}
This method fills \texttt{*pobj} with its \texttt{ownersIV} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_solvemap ( BridgeMPI *bridge, SolveMap **pobj ) ;
\end{verbatim}
\index{BridgeMPI_solvemap@{\tt BridgeMPI\_solvemap()}}
This method fills \texttt{*pobj} with its \texttt{solvemap} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_vtxmapIV ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_vtxmapIV@{\tt BridgeMPI\_vtxmapIV()}}
This method fills \texttt{*pobj} with its \texttt{vtxmapIV} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_rowmapIV ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_rowmapIV@{\tt BridgeMPI\_rowmapIV()}}
This method fills \texttt{*pobj} with its \texttt{rowmapIV} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_ownedColumns ( BridgeMPI *bridge, IV **pobj ) ;
\end{verbatim}
\index{BridgeMPI_ownedColumns@{\tt BridgeMPI\_ownedColumns()}}
This method fills \texttt{*pobj} with its \texttt{ownedColumnsIV} 
pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_Xloc ( BridgeMPI *bridge, DenseMtx **pobj ) ;
\end{verbatim}
\index{BridgeMPI_Xloc@{\tt BridgeMPI\_Xloc()}}
This method fills \texttt{*pobj} with its \texttt{Xloc} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_Yloc ( BridgeMPI *bridge, DenseMtx **pobj ) ;
\end{verbatim}
\index{BridgeMPI_Yloc@{\tt BridgeMPI\_Yloc()}}
This method fills \texttt{*pobj} with its \texttt{Yloc} pointer.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pobj} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_nproc ( BridgeMPI *bridge, int *pnproc ) ;
\end{verbatim}
\index{BridgeMPI_nproc@{\tt BridgeMPI\_nproc()}}
This method fills \texttt{*pobj} with the number of processors.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pnproc} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_myid ( BridgeMPI *bridge, int *pmyid ) ;
\end{verbatim}
\index{BridgeMPI_myid@{\tt BridgeMPI\_myid()}}
This method fills \texttt{*pobj} with the id of this processor.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{pmyid} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_lookahead ( BridgeMPI *bridge, int *plookahead ) ;
\end{verbatim}
\index{BridgeMPI_lookahead@{\tt BridgeMPI\_lookahead()}}
This method fills \texttt{*pobj} with the lookahead parameter.
\par \noindent {\it Return value:}
1 for a normal return, 
-1 if \texttt{bridge} is \texttt{NULL}.
-2 if \texttt{plookahead} is \texttt{NULL}.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Parameter methods}
\label{subsection:BridgeMPI:proto:parameters}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setMatrixParams ( BridgeMPI *bridge, int neqns, int type, int symmetryflag ) ;
\end{verbatim}
\index{BridgeMPI_setMatrixParams@{\tt BridgeMPI\_setMatrixParams()}}
This method sets the number of equations, type of entries, 
and symmetry type of the matrix.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{neqns} $\le$ 0
\end{tabular}
\begin{tabular}{ll}
-3 & \texttt{type} is invalid \\
-4 & \texttt{symmetryflag} is invalid \\
-5 & symmetry flag is Hermitian but type is real
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setMPIparams ( BridgeMPI *bridge, int nproc, int myid, MPI_Comm comm ) ;
\end{verbatim}
\index{BridgeMPI_setMPIparams@{\tt BridgeMPI\_setMPIparams()}}
This method sets the MPI environment parameters.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL}
\end{tabular}
\begin{tabular}{ll}
-2 & \texttt{nproc} $\le$ 0 \\
-3 & \texttt{myid} $<$ 0 or $>=$ \texttt{nproc}
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setOrderingParams ( BridgeMPI *bridge, int maxdomainsize, int maxnzeros, 
                               int maxsize, int seed, double compressCutoff ) ;
\end{verbatim}
\index{BridgeMPI_setOrderingParams@{\tt BridgeMPI\_setOrderingParams()}}
This method sets parameters needed for the ordering.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{maxdomainsize} $\le$ 0
\end{tabular}
\begin{tabular}{ll}
-3 & \texttt{maxsize} $\le$ 0 \\
-4 & \texttt{compressCutoff} $>$ 1
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setFactorParams ( BridgeMPI *bridge, int sparsityflag, int pivotingflag, 
              double tau, double droptol, int lookahead, PatchAndGoInfo *patchinfo ) ;
\end{verbatim}
\index{BridgeMPI_setFactorParams@{\tt BridgeMPI\_setFactorParams()}}
This method sets parameters needed for the factorization.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{sparsityflag} is invalid \\
-3 & \texttt{pivotingflag} is invalid 
\end{tabular}
\begin{tabular}{ll}
-4 & \texttt{tau} $<$ 2.0 \\
-5 & \texttt{droptol} $<$ 0.0 \\
-6 & \texttt{lookahead} $<$ 0
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setMessagesInfo ( BridgeMPI *bridge, int msglvl, FILE *msgFile ) ;
\end{verbatim}
\index{BridgeMPI_setMessagesInfo@{\tt BridgeMPI\_setMessagesInfo()}}
This method sets the message level and file.
\par \noindent {\it Return value:}
1 for a  normal return,
-1 if \texttt{bridge} is \texttt{NULL},
-2 if \texttt{msglvl} $>$ 0 and \texttt{msgFile} is \texttt{NULL}.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Setup methods}
\label{subsection:BridgeMPI:proto:setup}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_setup ( BridgeMPI *bridge, InpMtx *mtxA ) ;
\end{verbatim}
\index{BridgeMPI_setup@{\tt BridgeMPI\_setup()}}
This method orders the graph, generates the front tree, computes
the symbolic factorization, and creates the two permutation vectors.
\par \noindent {\it Return value:}
1 for a  normal return,
-1 if \texttt{bridge} is \texttt{NULL},
-2 if \texttt{mtxA} is \texttt{NULL}.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_factorStats ( BridgeMPI *bridge, int type, int symmetryflag, int *pnfront,
      int *pnfactorind, int *pnfactorent, int *pnsolveops, double *pnfactorops ) ;
\end{verbatim}
\index{BridgeMPI_factorStats@{\tt BridgeMPI\_factorStats()}}
This method takes as input the type and symmetry of the matrix,
and fills the pointer fields with the number of fronts, factor
indices, factor entries, forward and back solve operations,
and factor operations.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{type} is invalid \\
-3 & \texttt{symmetryflag} is invalid \\
-4 & \texttt{type} is real but \texttt{symmetryflag} is Hermitian \\
-5 & front tree is not present
\end{tabular}
\begin{tabular}{ll}
~-6 & \texttt{pnfront} is \texttt{NULL}  \\
~-7 & \texttt{pnfactorind} is \texttt{NULL}  \\
~-8 & \texttt{pnfactorent} is \texttt{NULL}  \\
~-9 & \texttt{pnsolveops} is \texttt{NULL}  \\
-10 & \texttt{pnfactorops} is \texttt{NULL} 
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Factor methods}
\label{subsection:BridgeMPI:proto:factor}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_factorSetup ( BridgeMPI *bridge, int maptype, double cutoff ) ;
\end{verbatim}
\index{BridgeMPI_factorSetup@{\tt BridgeMPI\_factorSetup()}}
This method constructs the map from fronts to owning processors, and
computes the number of factor operations that each thread will execute.
The \texttt{maptype} parameter can be one of four values:
\begin{itemize}
\item 1 --- wrap map
\item 2 --- balanced map
\item 3 --- subtree-subset map
\item 4 --- domain decomposition map
\end{itemize}
The wrap map and balanced map are not recommended.
The subtree-subset map is a good map with a very well balanced
nested dissection ordering.
The domain decomposition map is recommended when the nested
dissection tree is imbalanced or for the multisection ordering.
The domain decomposition map requires a \texttt{cutoff} parameter
in $\left \lbrack0,1\right \rbrack$ 
which specifies the relative size of a subtree that forms a domain.
If \texttt{maptype} is not one of 1, 2, 3 or 4, the default map is
used: domain decomposition with
\texttt{cutoff} = 1/(2*\texttt{nthread}).
\par \noindent {\it Return value:}
1 normal return, factorization did complete,
-1 \texttt{bridge} is \texttt{NULL},
-2 \texttt{frontETree} is not present.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_factor ( BridgeMPI *bridge, InpMtx *mtxA, int permuteflag, int *perror ) ;
\end{verbatim}
\index{BridgeMPI_factor@{\tt BridgeMPI\_factor()}}
This method permutes the matrix into the new ordering (if
\texttt{permuteflag} is 1), factors the matrix, and then
post-processes the factors.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return, factorization did complete \\
~0 & factorization did not complete \\
\end{tabular}
\begin{tabular}{ll}
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{mtxA} is \texttt{NULL} \\
-3 & \texttt{perror} is \texttt{NULL} \\
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Solve methods}
\label{subsection:BridgeMPI:proto:solve}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_solveSetup ( BridgeMPI *bridge ) ;
\end{verbatim}
\index{BridgeMPI_solveSetup@{\tt BridgeMPI\_solveSetup()}}
This method creates the {\tt SolveMap} object that governs the
parallel solve.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL}
\end{tabular}
\begin{tabular}{ll}
-2 & \texttt{frontMtx} is \texttt{NULL} \\
-3 & \texttt{frontMtx} needs to be postprocessed
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int BridgeMPI_solve ( BridgeMPI *bridge, int permuteflag, DenseMtx *mtxX, DenseMtx *mtxY ) ;
\end{verbatim}
\index{BridgeMPI_solve@{\tt BridgeMPI\_solve()}}
If \texttt{permuteflag} is 1, then \texttt{mtxY} is permuted into
the new ordering.
The linear system $AX = Y$ is solved.
If \texttt{permuteflag} is 1, then \texttt{mtxX} is permuted into
the old ordering.
\par \noindent {\it Return value:}
\begin{center}
\begin{tabular}{ll}
~1 & normal return \\
-1 & \texttt{bridge} is \texttt{NULL} \\
-2 & \texttt{X} is \texttt{NULL} \\
-3 & \texttt{Y} is \texttt{NULL} \\
\end{tabular}
\begin{tabular}{ll}
-4 & \texttt{frontmtx} is \texttt{NULL} \\
-5 & \texttt{mtxmanager} is \texttt{NULL} \\
-6 & \texttt{oldToNewIV} needed, but not available \\
-7 & \texttt{newToOldIV} needed, but not available \\
\end{tabular}
\end{center}
%-----------------------------------------------------------------------
\end{enumerate}
