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to try to duplicate it.  Instead, our decision has been to build upon
MATLAB itself and produce a prototype that users can try as
an extension to their current work rather than an alternative to it.
As mentioned, this approach
has also been followed by the Rostock/Wismar and Wake Forest
University projects, using
PVM or another message passing system rather than MPI.

<P><BR><P>
<H2>6. Conclusions</H2>
MultiMATLAB can be summarized in a few words.
We run MATLAB processes on multiple processors, with full
access to all the usual capabilities such as Toolboxes.
These processes communicate via simple MATLAB-style commands built
on MPI, with all message-passing details hidden as far as possible
from the user.  Both master/slave and SPMD paradigms are implemented, and
attention is paid to multiprocessor graphics.
All of this happens without any changes in the MATLAB architecture;
indeed, we have not had access to the MATLAB source code.
<P>

It is a straightforward matter to install our current software
on any network of Unix workstations or
SP2 system, provided that all the nodes are licensed to
run MATLAB and there is a shared file system.
We expect that extensions to networks of
PCs running Windows, based on appropriate implementations of MPI,
are not far behind.  We hope to make our research code
publicly available in the near future and will announce this
event on the NA-Net electronic distribution list and elsewhere.
Based on reactions of users so far, we think that MultiMATLAB
will prove appealing to many people, both for enhancing the
power of their computations and as an educational device for teaching
message passing ideas and parallel algorithms.
It gives MATLAB users easy access to message
passing, here and now.  The parallel efficiency is not always
as high as might be achieved, but for many applications it is
surprisingly good.  We hope to address questions of performance
in more detail in a forthcoming technical report.
<P>

MultiMATLAB is by no means in its final form.  This is an evolving
project, and various improvements in functionality,
for example in the areas of collective communications and
higher-level abstractions, are under development.
The current system also needs improvement in the area of robustness
with respect to various kinds of errors,
and in its documentation.
We are guided in the development process by several
projects underway in which MultiMATLAB is being
used by our colleagues for scientific computations.
<P>

As we have mentioned in the text, several projects related to
MultiMATLAB are being pursued at other institutions,
including CONLAB, FALCON, the Parallel
Toolbox, and others.  Though the details of what will emerge
in the next few years are of course not yet clear, we believe that the authors of
all of these systems join us in expecting that it is inevitable
that the MATLAB world will soon take the step from single
to multiple processors.

<HR>

<P><BR><P>
<H2>References</H2>

&#160;<A NAME="ref_polaris">[1]</A>
W. Blume, et al.
Effective Automatic Parallelization with Polaris.
International Journal of Parallel Programming. May 1995.
<P>

&#160;<A NAME="ref_falcon">[2]</A> L. De Rose, et al.
FALCON: An environment for the development of scientific libraries
and applications.  Proc. First Intl. Workshop on Knowledge-Based
Systems for the (re)Use of Program Libraries, Sophia Antipolis,
France, November 1995.
<P>

&#160;<A NAME="ref_falcon2">[3]</A> L. De Rose, et al.
FALCON: A MATLAB interactive restructuring compiler.
In Languages and Compilers for Parallel Computing, pp. 269-288.
Springer-Verlag.  August, 1995.
<P>

&#160;<A NAME="ref_conlab">[4]</A> P. Drakenberg, P. Jacobson, and
B. K&aring;gstr&ouml;m.
A CONLAB compiler for a distributed memory multicomputer.
R. F. Sincovec, et al., eds.,
Proc. Sixth SIAM Conf. Parallel Proc. for Sci. Comp., v. 2,
pp. 814-821. 1993.
<P>

&#160;<A NAME="ref_picl">[5]</A> G. A Geist, et al.
PICL: A portable instrumented communication library.
Tech. Rep. ORNL/TM-11130, Oak Ridge Natl. Lab., 1990.
<P>

&#160;<A NAME="ref_mpich">[6]</A>
W. Gropp, E. Lusk, N. Doss, and A. Skjellum.
A high-performance, portable implementation of the MPI
message passing interface standard.  Parallel Computing, to appear.
<P>

&#160;<A NAME="ref_mpibook">[7]</A>
W. Gropp, E. Lusk,  and A. Skjellum.
Using MPI.  MIT Press.  1994.
<P>

&#160;<A NAME="ref_pt">[8]</A> J. Hollingsworth, K. Liu, and Paul Pauca.
<!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><A HREF=http://www.mthcsc.wfu.edu/pt/pt.html>Parallel Toolbox
for MATLAB PT v. 1.00: Manual and Reference
Pages</A>.
Wake Forest University. 1996.
<P>

&#160;<A NAME="ref_isi">[9]</A> Integrated Sensors, Inc. home
page: http://www.sensors.com.
<P>

&#160;<A NAME="ref_conlab2">[10]</A> P. Jacobson,
B. K&aring;gstr&ouml;m, and M. R&auml;nnar. Algorithm development for distributed memory
multicomputers using CONLAB.
Scientific Programming, v. 1, pp. 185-203.  1992.
<P>

&#160;<A NAME="ref_alpha">[11]</A> J. Kadlec and N. Nakhaee.
<!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><A HREF=http://www.mathworks.com/Abstracts.html>Alpha Bridge, parallel processing under MATLAB.</A>
Second MathWorks Conference. 1995.
<P>

&#160;<A NAME="ref_matcom">[12]</A> MATCOM, March 1996 release.
http://techunix.technion.ac.il/~yak/matcom.html.
<P>

&#160;<A NAME="ref_mpi">[13]</A> 
Message Passing Interface Forum. MPI: A message-passing interface
standard.  Intl. J. Supercomputer Applics., v. 8. 1994.
<P>

&#160;<A NAME="ref_moler">[14]</A> C. Moler.
<!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><A HREF=http://www.mathworks.com/newsletter/spr95.html>Why there isn't a parallel
MATLAB</A>.
MathWorks Newsletter. Spring, 1995.
<P>

&#160;<A NAME="ref_rostock">[15]</A> S. Pawletta, T. Pawletta, and W. Drewelow.
Distributed and parallel simulation in an interactive environment.
Preprint, University of Rostock, Germany.  1995.
<P>

&#160;<A NAME="ref_rostock2">[16]</A> S. Pawletta, T. Pawletta, and W. Drewelow.
Comparison of parallel simulation techniques -- MATLAB/PSI.
Simulation News Europe, v. 13, pp. 38-39. 1995.
<P>

&#160;<A NAME="ref_trefethen">[17]</A> 
L. N. Trefethen. Pseudospectra of matrices.
In D. F. Griffiths and G. A. Watson, Numerical Analysis 1991,
Longman, pp. 234--266. 1992.

<P><BR><P>
<H3>About the Authors</H3>

<!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><A HREF=http://www.tc.cornell.edu/~anne>Anne Trefethen</A>
is Associate Director for Scientific Computational
Support at the Cornell Theory Center.  From 1988 to 1992 she
worked at Thinking Machines, Inc., where she was one of the developers
of the Connection Machine Scientific Software Library.
<P>

<!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><A HREF=http://www.cs.cornell.edu/Info/People/vsm>Vijay Menon</A>,
interested in parallelizing compilers, is a PhD student of
<!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><A HREF=http://www.cs.cornell.edu/Info/Department/Annual95/Faculty/Pingali.html>Keshav
Pingali</A>
in the Computer Science Department at Cornell.
<P>

<!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><A HREF=http://www.cs.cornell.edu/Info/People/chichao/chichao.html>Chi-Chao Chang</A>
and <!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><A HREF=http://www.cs.cornell.edu/Info/People/grzes/grzes.html>Greg Czajkowski</A>,
interested in runtime systems, are PhD students of
<!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><A HREF=http://www.cs.cornell.edu/Info/People/tve/tve.html>Thorsten von Eicken</A>
in the Computer Science Department at Cornell.
<P>

<!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><A HREF=http://www.tc.cornell.edu/CSERG/myers>Chris Myers</A>
is a Research Scientist
at the Cornell Theory Center.  His research interests are in
condensed matter physics and scientific computing.
<P>

<!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><!WA40><A HREF=http://www.cs.cornell.edu/home/lnt>Nick Trefethen</A>,
a Professor in the Department of
Computer Science at Cornell, has been using MATLAB since 1980.
His research interests are in
numerical analysis and applied mathematics.

<P><BR><P>
<H3>Acknowledgments</H3>

For advice and comments concerning both the MultiMATLAB project
and this paper, we are grateful to 
<!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><!WA41><A HREF=http://cam.cornell.edu/~driscoll/index.html>Toby Driscoll</A>,
<!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><!WA42><A HREF=http://www.mcs.anl.gov/people/gropp/index.html>Bill Gropp</A>,
<!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><!WA43><A HREF=http://www.cs.cornell.edu/Info/People/xliu/home.html>Xiaoming Liu</A>,
<!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><!WA44><A HREF=http://www.mathworks.com/images/cleve_moler.gif>Cleve Moler</A>,
<!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><!WA45><A HREF=http://www.mcs.anl.gov/people/bsmith/index.html>Barry Smith</A>,
<!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><!WA46><A HREF=http://www.cs.cornell.edu/Info/People/vavasis/vavasis.html>Steve Vavasis</A>,
and
<!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><!WA47><A HREF=http://www.cs.cornell.edu/Info/People/tve/tve.html>Thorsten von Eicken</A>.
<P>

This research was supported in part by The MathWorks, Inc.
It was conducted in part using the resources of the Cornell
Theory Center, which receives major funding from the National
Science Foundation (NSF) and New York State, with additional
support from the Defence Advanced Research Projects Agency (DARPA),
the National Center for Research Resources at the National
Institutes of Health (NIH), IBM Corporation, and other members
of the center's Corporate Partnership Program.  
Further support has been provided by
NSF Grant DMS-9500975 and
DOE Grant DE-FGO2-94ER25199 (L. N. Trefethen),
NSF Grant CCR 9503199 (support of Menon by Pingali),
ARPA Grant N00014-95-1-0977 (support of Czajkowski by von Eicken)
and a Doctoral Fellowship (200812/94-7) from the Brazilian Research
Council (Chang).

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