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<H2><A NAME="SECTION04445000000000000000">Array Descriptor for Narrow Band and Tridiagonal Matrices</A></H2>
<P>
<A NAME="secdesc501"> </A>
<P>
The array descriptor <B>DESC_</B>
whose type is defined as
<B>DESC_(DTYPE_)=501</B><A NAME="3185"> </A>,
is an integer array of length 7.
This descriptor type is used in
the ScaLAPACK narrow band routines
and tridiagonal routines to specify
a block-column distribution of a
global array over a one-dimensional
process grid. In the general and
symmetric positive definite banded
and tridiagonal routines, a
one-dimensional block-column
distribution is specified for
the coefficient matrix<A NAME="3186"> </A>.
The matrix of right-hand-side
vectors must be distributed
over a one-dimensional process
grid using a block-row data
distribution. Refer to
section <A HREF="node82.html#sec1dbd">4.4.1</A>
for further details on block
data distribution.
<P>
Let us assume, for example,
that we have an array descriptor
<I>DESCA</I> for a block-column
distributed array <I>A</I>. For
readability of the code, we
have associated symbolic names
with the descriptor entries.
As previously mentioned, the
notations x_ used in the
entries of the array descriptor
denote the attributes of a
global array. For readability
of the code, we have associated
symbolic names for the descriptor
entries. For example, N_
denotes the number of columns
and N_A specifically denotes
the number of columns in global
array <I>A</I>.
<P>
<P><A NAME="3189"> </A><IMG WIDTH=655 HEIGHT=414 ALIGN=BOTTOM ALT="table3188" SRC="img354.gif"><BR>
<STRONG>Table 4.11:</STRONG> Content of the array descriptor for in-core narrow band
and tridiagonal coefficient matrices<BR>
<P>
<P>
When <I>A</I> is non-symmetric and
factorized without pivoting,
<A NAME="3197"> </A><A NAME="3198"> </A><A NAME="3199"> </A><A NAME="3200"> </A>
LLD_A must be at least
<I>BWL</I>+1+<I>BWU</I>. When <I>A</I> is
non-symmetric and factorized
with partial pivoting, LLD_A
<A NAME="3201"> </A><A NAME="3202"> </A><A NAME="3203"> </A><A NAME="3204"> </A>
must be at least 2(<I>BWL</I>+<I>BWU</I>)+1.
When <I>A</I> is symmetric positive
definite, LLD_A must be at least
<A NAME="3205"> </A><A NAME="3206"> </A><A NAME="3207"> </A><A NAME="3208"> </A>
<I>BW</I>+1. Finally, when <I>A</I> is
tridiagonal, LLD_A is not
<A NAME="3209"> </A><A NAME="3210"> </A><A NAME="3211"> </A><A NAME="3212"> </A>
referenced.
<P>
<BR> <HR>
<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
</ADDRESS>
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