[Trilinos-Users] [EXTERNAL] Re: direct invertion of a projected matrix (Amesos and Epetra_CrsMatrix?)

[Denis Davydov]

Dear Mike and Siva,

Thanks for the prompt reply.

Problem sizes I have in mind are from few hundreds (test case with full matrices without accounting for sparsity) to 
few thousands (planned actual runs with sparse matrices, roughly up to 100 non-zero elements per row).

I understand that the performance will not be ideal, yet I assume it should be comparable to what I would get
by using ScaLAPACK directly with full matrices to do LU factorization with MPI, right?
And most importantly it should be better than what I currently have: 
a completely sequential matrix with its serial inverse on each MPI core using Lapack.

p.s. for this application I consider direct solvers because (i) ScaLAPACK was used by other researchers in the same context; 
(ii) matrix size is still small compared to the index space of FE and I need to use the inverse of a single matrix several times
in different parts of the algorithm.

Regards,
Denis.

> On 22 Mar 2017, at 01:11, Rajamanickam, Sivasankaran <srajama at sandia.gov> wrote:
> 
> Denis,
>   As Mike said, the performance may not be what you want. Depending on the problem size, number of MPI ranks and number of factorizations vs number of solvers, you might be better of creating distributed sparse matrix and still use a simple sequential sparse solver (assuming memory is not a bottleneck).  The asymptotic number of operations will come into play very quickly in this case.
> 
> -Siva
>  
> From: Trilinos-Users <trilinos-users-bounces at trilinos.org> on behalf of Heroux, Michael A <maherou at sandia.gov>
> Sent: Tuesday, March 21, 2017 6:01 PM
> To: Denis Davydov; trilinos-users
> Subject: [EXTERNAL] Re: [Trilinos-Users] direct invertion of a projected matrix (Amesos and Epetra_CrsMatrix?)
>  
> ​*Performance will be quite poor, I think.
> From: Trilinos-Users <trilinos-users-bounces at trilinos.org> on behalf of Heroux, Michael A <maherou at sandia.gov>
> Sent: Tuesday, March 21, 2017 6:43 PM
> To: Denis Davydov; trilinos-users
> Subject: [EXTERNAL] Re: [Trilinos-Users] direct invertion of a projected matrix (Amesos and Epetra_CrsMatrix?)
>  
> Denis,
> 
> You can store a full matrix as a Epetra_CrsMatrix and use Amesos.  Performance will be quite, I think.​
> 
> Can you give more details about the dimensions of the problems?
> 
> Also, are you using an optimized BLAS for your LAPACK computations?
> 
> Mike
> 
> From: Trilinos-Users <trilinos-users-bounces at trilinos.org> on behalf of Denis Davydov <davydden at gmail.com>
> Sent: Tuesday, March 21, 2017 9:38 AM
> To: trilinos-users
> Subject: [EXTERNAL] [Trilinos-Users] direct invertion of a projected matrix (Amesos and Epetra_CrsMatrix?)
>  
> Dear all,
> 
> I would like to have a MPI-parallel inversion of (eventually sparse) matrix of size N being several hundreds.
> I put “sparse” in brackets, because for starters i need to consider it full. The matrix represents the 
> projection of a FE operator on a vector subspace. I guess something similar is probably done in 
> Anasazi in the context of eigensolvers.
> 
> So the main question is if I can use Epetra_CrsMatrix but for now set the sparsity to be full?
> If that is possible, i suppose i should be able to use Amesos direct solvers to get LU factorization
> of the matrix (say using ScaLAPACK) and then do whatever I want with it.
> 
> If there are other classes in Trilinos to do the job better, please let me know.
> 
> p.s. currently i do inversion in serial, eventually using Lapack, but this takes too much time.
> 
> Sincerely,
> Denis.
> 
> 

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