[petsc-users] an ambiguity on a Lanczos solver for a symmetric system -- advice needed

[Umut Tabak]

Dear all,

I am experiencing lately some issues with a symmetric Lanczos 
eigensolver in FORTRAN. Basically, I have test code in MATLAB where I am 
using HSL_MA97(MATLAB interface) at the moment

When I program Lanczos iterations in blocks in MATLAB by using HSL_MA97, 
as expected my overall solution time decreases meaning that block 
solution improves the solution efficiency.

Then, to apply the same algorithm on problems on the orders of millions, 
I am transferring the same algorithm to a FORTRAN code but this time 
with MUMPS as the solver then I was expecting the solution time to 
decrease as well, but my overall solution times are increasing when I 
increase the block size.

For a check with MUMPS, I only tried the block solution phase and 
compared 120 single solutions to

60 solutions by blocks of 2
30 solutions by blocks of 4
20 solutions by blocks of 6
15 solutions by blocks of 8

and saw that the total solution time in comparison to single solves are 
decreasing so I am thinking this is not the source of the problem, I 
believe.

What I am doing is that I am performing a full reorthogonalization in 
the Lanczos loop, which includes some dgemm calls and moreover there are 
some other calls for sparse symmetric matrix vector multiplications from 
Intel MKL.

I could not really understand why the overall solution time is 
increasing with the increase of the block sizes in FORTRAN whereas I was 
expecting even an improvement over my MATLAB code.

Any ideas on what could be going wrong.

Best regards and thanks in advance,

Umut