On Sat, Sep 13, 2014 at 11:28 AM, Erik Slivken
<> wrote:
> William-
>
> I am trying to find the eigenvalues of a roughly 10000x10000 sparse matrix
> with entries from {0,1} (and would like to do this for even larger
> matrices). I don't know what could be done to increase the speed (right now
> it has been running for roughly half a day). But it said to email you to
> raise a quota. Also, if there is special faculty access, this is a project
> with Chris Hoffman from UW and I am sure he would sign on for more computing
> power.
>
> Thanks for your time.
>
> Cheers,
> Erik Slivken
>
> P.S. How long should it take to find the eigenvalues of a 10000x10000
> sparse matrix with entries from {0,1}? What about a 10^6x10^6 sparse matrix
> with entries in from {0,1}?
Never. Sage doesn't have any easily available sophisticated sparse
linear algebra algorithms, as far as I know. Linbox (which is in Sage
-- a C++ library), might have something; and Cremona's eclib has some
gems hidden in it. I wrote some really stupid sparse linear algebra,
which was sufficient for something I did once. There's several
stages to sparse algorithms, and what is in Sage only implements the
first part -- the "endgame", which is to solve a resulting dense
system at a certain point, isn't in sage. Sebastian Pancratz and I
did implement it once
somewhere... (not sure), but it isn't in sage (and it was not easy),
and now Sebastian works at a bank.
Try typing
set_verbose(2)
to see what is happening, if you're using sage.
You should seriously consider searching the web for current available
software for sparse linear algebra. Last I checked, unfortunately,
Sage is definitely not an off-the-shelf solution for anything
nontrivial involving sparse matrices, except for maybe efficiently
storing them.
(I've changed the subject and cc'd some people on this email, in case
anybody knows anything about sparse linear algebra and wants to chime
in.)
William
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
wst...@uw.edu
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