[petsc-users] Will using SBAIJ to solve for all eigenvalues and eigenvectors of a symmetric sparse matrix produced one row at a time be beneficial ?

[Shitij Bhargava]

Oh, ok, i have verified that matrix assembly is not taking so long. The
bottleneck was something else. But now I have encountered a different, more
important problem regarding the solver itself, which I suppose I should ask
in a different thread.

Thank you.


Shitij

On 30 July 2011 21:56, Matthew Knepley <knepley at gmail.com> wrote:

> On Sat, Jul 30, 2011 at 11:11 AM, Shitij Bhargava <shitij.cse at gmail.com>wrote:
>
>> Hi !!
>>
>> I have just started using SLEPc/PETSc.
>>
>> The problem that I am trying to solve is that I have some routines
>> calculating one row at a time of a matrix, which I want to insert in some
>> sparse matrix representation, and then find the next row, insert it, and so
>> on. (This is being done to avoid the need to have one big NxN matrix in
>> memory).The matrix is also symmetric, so the row that the subroutines
>> produce is such that any non-zero element can be present only in that part
>> of the row corresponding to the upper triangle of the matrix. (all others
>> are zero). After I have the matrix in sparse format, I want to find all the
>> eigenvalues and eigenvectors.
>>
>> Till now I have been using the SeqAij matrix and MatSetValues method with
>> preallocation set appropriately, but I am not satisfied with its performance
>> (the way I am doing it). When one row is produced, I insert it into the AIJ
>> matrix, so there are total of N calls to MatSetValues. Also even though the
>> matrix is symmetric, i have to enter the full matrix, as otherwise the
>> eigensolver doesnt seem to produce the right answer (Why ? I set the problem
>> type to EPS_HEP, but still it requires me to store the full matrix ? It is
>> written in documentation that problem type should always be specified so
>> that the eigensolver can take advantage of it (symmetry in this case), but
>> considering that I still have to store the full matrix, it meant 'advantage'
>> only in time, not memory ?....when I set the problem type to EPS_HEP, it
>> means that it will take only the upper or lower triangle right ? why should
>> it require both ? Is this because the matrix type is not symmetric, unlike
>> SBAIJ ?)
>>
>
> You must set the type to SBAIJ in order to enter only the symmetric part.
>
>
>> So, if I use SBAIJ and say, enter some bs rows at a time into the SBAIJ
>> matrix, will it be faster ? Also, in that case would I still have to enter
>> both upper and lower triangle or only one (I hope only one, otherwise the
>> 'S' doesnt make sense to me, but in that case, which one ? The eigensolver
>> doesnt give me an option to specify if the upper or lower triangle is stored
>> in the matrix in case the problem type is EPS_HEP). Will the eigensolver
>> produce the right answers in this case ? (say, storing only upper triangle
>> in SBAIJ, instead of both)
>>
>
> I do not think it will be noticeably faster. Value entry is usually not a
> large part of the time. YOu can check this using -log_summary.
>
>
> http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/Mat/MATSEQSBAIJ.html#MATSEQSBAIJ
>
> show that only the upper triangle is stored.
>
>
>> Otherwise, while using AIJ, if I insert multiple rows at a time instead of
>> just one (thus reducing the number of calls to MatSetValues, at the cost of
>> more memory), will this be much beneficial ? (Please note that the matrix is
>> not very sparse)
>>
>
> I cannot say anything until we see the timing from -log_summary. It is very
> rare that matrix construction is a factor,
> if it has been properly allocated, which you can check using -info.
>
>    Matt
>
>
>> Thank you very much in advance !!!
>>
>>
>> Shitij
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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