Dear Hong,

On Wed, Dec 28, 2016 at 4:42 PM, Hong <hzhang@mcs.anl.gov> wrote:

Vijay:
The performance of eigenvalue computation depends on many factors
- matrix features, location of eigenvalues, orthogonalization of eigenvectors
- how many eigensolutions do you compute, largest/smallest spectrum, accuracy
- algorithms used
- computer used ...

I've used the krylovshur solver from SLEPc.

I've asked for two lowest roots within the 1e-10 error bar.

The matrix has at most 48 nonzero elements per row.

Here are some details about the cluster:

Processor: Intel(r) IVYBRIDGE 2,8 Ghz 10 (bisocket)

Ram : 64Gb

Interconnection: Infiniband (Full Data Rate ~ 6.89Gb/s)

I'm doing exact diagonalization studies of some phenomenological model Hamiltonian. In this study I have to diagonalize large sparse matrices in Hilbert space of Slater determinants many times.
Why do you carry out these experiments? For solving this type of problem, I would suggest searching related research publications and compare your results.

I'm using a variant of the traditional Double Exchange Hamiltonian.

I'm interested in a specific part of the parameter space which is not fully explored in the literature. In this region the low energy spectrum is unusually dense (thus the exact diagonalization technique.) To my knowledge such a set of parameters has not been explored before.

Hope this answers your question...

Thanks,

Vijay

I've successfully used PETSc + SLEPc to get few smallest eigenvalues.
For example I've been able to diagonalize a matrix of rank 91454220 with 990 processors. This diagonalization took 15328.695847 Sec (or 4.25 Hrs.)

The matrix size 91M is quite amazing.

Hong

I have two questions:

1. Is this time reasonable, if not, is it possible to optimize further ?

2. I've tried a quick google search but could not find a comprehensive benchmarking of the SLEPc library for sparse matrix diagonalization. Could you point me to a publication/resource which has such a benchmarking ?

Thanks for your help.

PETSc Version: master branch commit: b33322e
SLEPc Version: master branch commit: c596d1c

Best,
Vijay