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<H2><A NAME="SECTION04467000000000000000">Alignment Restrictions</A></H2>
<A NAME="3523"> </A><A NAME="3524"> </A>
<A NAME="alignment"> </A>
<P>
Most routines in the present ScaLAPACK
library have <EM>alignment restrictions</EM>.
Alignment restrictions are constraints
in the type of distributions and the
indexing into the matrix that the user
may utilize when calling a particular
routine. For example, some routines
will not accept submatrices whose
starting index is not a multiple of
the physical blocking factor.
<P>
More commonly, routines require that
their various operand matrices have
certain alignment commonalities.
For instance, the solver routines
generally require that row <I>i</I> of
the matrix A be distributed across
the same process row as row <I>i</I> of
the right hand side matrix B.
<P>
Because of their idiosyncratic nature,
it is almost impossible to give a full
description of the alignment restrictions
inherit in the present library without
doing so on a routine-specific basis.
All ScaLAPACK routines provide a description
of the assumed alignment restrictions
in the leading comments to the routine,
and at this time the user must consult
the actual code to find out what
restrictions exist, if any.
<P>
We are working to remove the alignment
restrictions, (with the exceptions noted
below) so that the user will not have to
worry about alignment, save as a performance
issue.
<P>
Certain fundamental restrictions about
data distributions are not currently
being removed the library. Examples
include the fact that the operands
should be block-cyclicly distributed
for the dense codes and one-dimensional
block distributed for the banded codes.
Also included here is the restriction
that all operands be distributed across
the same context (process grid).
<P>
Note that the ScaLAPACK library
includes a redistribution/copy
routine which allows the user
to explicitly move matrices
across contexts. Similar routines
could be provided for distributions
that do not match the ones presently
employed in ScaLAPACK.
<P>
Finally, we note that the current
<EM>descriptor</EM> structure does
not accommodate the definition of
replicated vectors. A <EM>replicated</EM>
vector is a vector that is distributed
across a row or column within the
process grid and duplicated across
subsequent process rows or columns,
respectively. Such vectors occur,
for example, as the <TT>IPIV</TT><A NAME="3530"> </A>
vector in the LU factorization and
the <TT>TAU</TT><A NAME="3532"> </A>
vector in QR factorizations.
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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