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<H2><A NAME="SECTION04448000000000000000">Matrix Storage Conventions for Band and Tridiagonal Matrices</A></H2>
<P>
A general<A NAME="3352"> </A>
tridiagonal matrix of order <I>n</I> is stored globally
in three one-dimensional arrays <I>dl</I>, <I>d</I>, <I>du</I> of
length <I>n</I> containing the subdiagonal, diagonal,
and superdiagonal elements, respectively. Note
the mild change from LAPACK in which <I>dl</I> and
<I>du</I> were actually of global length <I>n</I>-1. To make
the distribution of the vectors consistent, we have
chosen to make them all of length <I>n</I>. Note that
<I>dl</I>(1)=<I>du</I>(<I>n</I>)=0.
<P>
Similarly, a symmetric<A NAME="3353"> </A>
tridiagonal matrix is stored globally in two
one-dimensional arrays <I>d</I>, <I>e</I> of length <I>n</I>
containing the diagonal and off-diagonal elements,
respectively. Again, there is a slight departure
from LAPACK in which <I>e</I> was of global length <I>n</I>-1.
Here, <I>e</I>(<I>n</I>)=0.
<P>
The vectors (<I>DL</I>, <I>D</I>, <I>DU</I>) or (<I>D</I>, <I>E</I>) representing
these matrices must be block distributed to a
one-dimensional process grid. These vectors can
be equivalently distributed block-row or block-column
since vectors are one-dimensional data structures.
Note that when inputting vectors to these special-purpose
low-diagonal routines, <TT>LLD_</TT> can be ignored,
since it is assumed that the local portions of the
vectors are of unit stride.
<P>
<BR> <HR>
<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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