dense hermitian eigendecomposition under shared memory

[mike669]

Hi all,

We're two students working on a parallel systems project, and we came to a bit of a problem. We'll appreciate any advise/lead on the topic.

We have a shared memory experimental platform with multiple (64-256) cores and shared 2M memory, and we're trying to find eigenvalues and eigenvectors for a dense 169*169 hermitian matrix in a parallel way.

We've looked at the scalapack documentation, but it doesn't say the storage requirements for each routine.

We're not Fortran experts, and either way we'll have to rewrite the code in C, but can you please point us to the most effective routine/algorithm for solving the problem.

Thanks!
Lior and Ami

[admin]

Lior and Ami
You may want to post your request on the PLASMA forum.
http://icl.cs.utk.edu/plasma/forum
Julie

[ltaief]

Dear Lior and Ami,
The PLASMA developer team is still working
on getting the eigensolvers run in parallel
on multicore systems. This is indeed a quite
challenging task.
Here are some details about one approach for the Sym eigenvalue problem:
1) Reduce first in parallel the matrix to band tridiagonal with nb+1 extra diagonals using some
fast kernels.
2) Further reduce the band form to the required tridiagonal form using the
SBR toolbox (software for successive band reductions). This step is sequential
3) Aggregate the reflectors to generate the unitary matrix needed to
compute the eigenvectors. This step is done in parallel.
4) Apply the QR algorithms to compute the eigenvalues and their
corresponding eigenvectors.
We have a double precision prototype which does 1), 2) and 3).
The item 4) is still under investigation to make it run in parallel.
The work has not yet been published.
You could also look at the LAPACK CHEEV routine which will describe
more precisely the algorithms.
Hope this helps!
Hatem

[mike669]

Thanks for the tips.

after further investigation, we'll implement the MRRR algorithm as it's the fastest and the least storage-demanding parallel algorithm we've found for finding all eigenpairs.

Thanks again,
Lior and Ami