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\par
\section{Data Structures}
\label{section:FrontMtx:dataStructure}
\par
The {\tt FrontMtx} structure has the following fields.
\begin{itemize}
\item
{\tt int nfront} : number of fronts.
\item
{\tt int neqns} : number of rows and columns in the factor matrix.
\item
{\tt int symmetryflag} : flag to denote the type of symmetry
of $A + \sigma B$.
\begin{itemize}
\item
{\tt SPOOLES\_SYMMETRIC} --- $A$ and/or $B$ are symmetric.
\item
{\tt SPOOLES\_HERMITIAN} --- $A$ and/or $B$ are hermitian.
\item
{\tt SPOOLES\_NONSYMMETRIC} --- $A$ and/or $B$ are nonsymmetric.
\end{itemize}
\item
{\tt int pivotingflag} : flag to specify pivoting for stability,
\begin{itemize}
\item
{\tt SPOOLES\_NO\_PIVOTING} --- pivoting not used
\item
{\tt SPOOLES\_PIVOTING} --- pivoting used
\end{itemize}
\item
{\tt int sparsityflag} : flag to specify storage of factors.
\begin{itemize}
\item
{\tt 0} --- each front is dense
\item
{\tt 1} --- a front may be sparse due to entries dropped
because they are below a drop tolerance.
\end{itemize}
\item
{\tt int dataMode} : flag to specify data storage.
\begin{itemize}
\item
{\tt 1} --- one-dimensional, used during the factorization.
\item
{\tt 2} --- two-dimensional, used during the solves.
\end{itemize}
\item
{\tt int nentD} : number of entries in $D$
\item
{\tt int nentL} : number of entries in $L$
\item
{\tt int nentU} : number of entries in $U$
\item
{\tt Tree *tree} : Tree object that holds the tree of fronts.
Note, normally this is {\tt frontETree->tree}, but we leave this
here for later enhancements where we change the tree after the
factorization, e.g., merge/drop fronts.
\item
{\tt ETree *frontETree} : elimination tree object that holds the
front tree.
\item
{\tt IVL *symbfacIVL} : {\tt IVL} object that holds the
symbolic factorization.
\item
{\tt IV *frontsizesIV} : {\tt IV} object that holds the
vector of front sizes, i.e., the number of internal rows
and columns in a front.
\item
{\tt IVL *rowadjIVL} : {\tt IVL} object that holds the
row list for the fronts, used only for a nonsymmetric factorization
with pivoting enabled.
\item
{\tt IVL *coladjIVL} : {\tt IVL} object that holds the
column list for the fronts, used only for a symmetric or
nonsymmetric factorization with pivoting enabled.
\item
{\tt IVL *lowerblockIVL} : {\tt IVL} object that holds the
front-to-front coupling in $L$, used only for a
nonsymmetric factorization.
\item
{\tt IVL *upperblockIVL} : {\tt IVL} object that holds the
front-to-front coupling in $U$.
\item
{\tt SubMtx **p\_mtxDJJ} : a vector of pointers to diagonal submatrices.
\item
{\tt SubMtx **p\_mtxUJJ} : a vector of pointers to submatrices in U
that are on the block diagonal, used only during the factorization.
\item
{\tt SubMtx **p\_mtxUJN} : a vector of pointers to submatrices in U
that are off the block diagonal, used only during the factorization.
\item
{\tt SubMtx **p\_mtxLJJ} : a vector of pointers to submatrices in L
that are on the block diagonal, used only during a nonsymmetric
factorization.
\item
{\tt SubMtx **p\_mtxLNJ} : a vector of pointers to submatrices in L
that are off the block diagonal, used only during a nonsymmetric
factorization.
\item
{\tt I2Ohash *lowerhash} : pointer to a {\tt I2Ohash} hash table
for submatrices in $L$, used during the solves.
\item
{\tt I2Ohash *upperhash} : pointer to a {\tt I2Ohash} hash table
for submatrices in $U$, used during the solves.
\item
{\tt SubMtxManager *manager} : pointer to an object that manages
the instances of submatrices during the factors and solves.
\item
{\tt Lock *lock} : pointer to a {\tt Lock} lock used
in a multithreaded environment to ensure exlusive access while
allocating storage in the {\tt IV} and {\tt IVL} objects.
This is not used in a serial or MPI environment.
\item
{\tt int nlocks} : number of times the lock has been locked.
\item
{\tt PatchAndGo *info} : this is a pointer to an object that is
used by the {\tt Chv} object during the factorization of a front.
\end{itemize}
\par
One can query the properties of the front matrix object
using these simple macros.
\begin{itemize}
\item
{\tt FRONTMTX\_IS\_REAL(frontmtx)} is {\tt 1} if {\tt frontmtx}
has real entries and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_COMPLEX(frontmtx)} is {\tt 1} if {\tt frontmtx}
has complex entries and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_SYMMETRIC(frontmtx)} is {\tt 1} if {\tt frontmtx}
comes from a symmetric matrix or linear combination of symmetric
matrices, and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_HERMITIAN(frontmtx)} is {\tt 1} if {\tt frontmtx}
comes from a Hermitian matrix or linear combination of Hermitian
matrices, and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_NONSYMMETRIC(frontmtx)} is {\tt 1} if {\tt frontmtx}
comes from a nonsymmetric matrix or linear combination of nonsymmetric
matrices, and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_DENSE\_FRONTS(frontmtx)} is {\tt 1}
if {\tt frontmtx}
comes from a direct factorization and so stores dense submatrices,
and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_SPARSE\_FRONTS(frontmtx)} is {\tt 1}
if {\tt frontmtx} comes from an approximate factorization
and so stores sparse submatrices, and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_PIVOTING(frontmtx)} is {\tt 1}
if pivoting was used during the factorization,
and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_1D\_MODE(frontmtx)} is {\tt 1}
if the factor are still stored as a one-dimensional data
decomposition (i.e., the matrix has not yet been post-processed),
and {\tt 0} otherwise.
\item
{\tt FRONTMTX\_IS\_2D\_MODE(frontmtx)} is {\tt 1}
if the factor are stored as a two-dimensional data
decomposition (i.e., the matrix has been post-processed),
and {\tt 0} otherwise.
\end{itemize}
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