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\par
\chapter{{\tt SubMtxList}: {\tt SubMtx} list object }
\par
This object was created to handle a list of lists of {\tt
SubMtx} objects during a matrix solve.
Its form and function is very close to the {\tt ChvList} object
that handles lists of lists of {\tt Chv} objects during the
factorization.
\par
Here are the main properties.
\begin{enumerate}
\item
There are a fixed number of lists, set when the {\tt SubMtxList}
object is initialized.
\item
For each list there is an expected count, the number of times an
object will be added to the list. (Note, a {\tt NULL} object can be
added to the list. In this case, nothing is added to the list,
but its count is decremented.)
\item
There is one lock for all the lists, but each list can be flagged
as necessary to lock or not necessary to lock before an insertion,
count decrement, or an extraction is made to the list.
\end{enumerate}
\par
The {\tt SubMtxList} object manages a number of lists
that may require handling critical sections of code.
For example, one thread may want to add an object to a particular
list while another thread is removing objects.
The critical sections are hidden inside the {\tt SubMtxList} object.
Our solve code do not know about any mutual exclusion
locks that govern access to the lists.
\par
There are four functions of the {\tt SubMtxList} object.
\begin{itemize}
\item
Is the incoming count for a list nonzero?
\item
Is a list nonempty?
\item
Add an object to a list (possibly a {\tt NULL} object) and
decrement the incoming count.
\item
Remove a subset of objects from a list.
\end{itemize}
The first two operations are queries, and can be done without
locking the list.
The third operation needs a lock only when two or more threads will
be inserting objects into the list.
The fourth operation requires a lock only when one thread will add
an object while another thread removes the object and the incoming
count is not yet zero.
\par
Having a lock associated with a {\tt SubMtxList} object is optional,
for example, it is not needed during a serial factorization nor a
MPI solve.
In the latter case there is one {\tt SubMtxList} per process.
For a multithreaded solve there is one {\tt SubMtxList}
object that is shared by all threads.
The mutual exclusion lock that is (optionally) embedded in the {\tt
SubMtxList} object is a {\tt Lock} object from this library.
It is inside the {\tt Lock} object that we have a
mutual exclusion lock.
Presently we support the Solaris and POSIX thread packages.
Porting the multithreaded codes to another platform should be
simple if the POSIX thread package is present.
Another type of thread package will require some modifications
to the {\tt Lock} object, but none to the {\tt SubMtxList} objects.
\par
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