[petsc-users] Why does CHOLMOD solution time differs between PETSc and MATLAB?
Victor Magri
victor.antonio.magri at gmail.com
Sun Nov 23 11:52:49 CST 2014
On Fri, Nov 21, 2014 at 4:49 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> Here is my conjecture (more than a guess, but less than a full statement
> of fact). CHOLMOD uses a "supernodel" algorithm which means that it works
> on dense blocks of the factored matrix and can take advantage of BLAS 2 and
> 3 operations (unlike almost everything in PETSc).
I though that PETSc would take more advantage from BLAS 2.
1) the MKL BLAS/LAPACK are likely much faster than the Fortran versions
Your conjecture was right! I compiled PETSc to use mkl.so from my Matlab
folder and run the tests again. The computational time was pretty the same
in comparison with MATLAB (See attached).
2) it is possible the MKL BLAS/LAPACK used by MATLAB use multiple threads
> to take advantage of multiple cores on the hardware.
At least in my computer, no. I opened the system monitor to see if MATLAB
would use more than one thread and it didn't.
I think CHOLMOD, used by MATLAB backslash operator, uses AMD (approximate
> min. degree) ordering scheme by default
Yes, I searched about that and it really does.
For PETSc + MATLAB, use the option -pc_factor_mat_ordering_type qmd
The computation time got bigger! I was thinking that reordering would make
it lower. Maybe it doesn't because this matrix comes from a 5-point
discretization stencil... I tried also RCM and ND but the best time came
from natural.
Thank you so much for helping, Barry and Abhyankar.
On Fri, Nov 21, 2014 at 6:34 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
> > On Nov 21, 2014, at 1:46 PM, Abhyankar, Shrirang G. <abhyshr at mcs.anl.gov>
> wrote:
> >
> > I think this may have to do with the matrix reodering scheme. I think
> CHOLMOD, used by MATLAB backslash operator, uses AMD (approximate min.
> degree) ordering scheme by default. PETSc's default reordering scheme is
> nested dissection. For PETSc + MATLAB, use the option
> -pc_factor_mat_ordering_type qmd
>
> This is possible and definitely worth trying with different orders, but
> I checked the nonzeros in the matrix and the L factor for both approaches
> and they are very similar
>
> PETSc call:
> Common.fl 1.81877e+10 (flop count from most recent
> analysis)
> Common.lnz 4.46748e+07 (fundamental nz in L)
>
> MatLab call:
> flop count: 1.8188e+10
> nnz(L): 4.4675e+07
>
> Unless I am misunderstanding something both factors likely look very
> similar.
>
> Barry
>
>
> >
> > Shri
> >
> > On Nov 21, 2014, at 11:23 AM, "Victor Magri" <
> victor.antonio.magri at gmail.com> wrote:
> >
> >> Hi,
> >>
> >> I'm solving a linear system which comes from the discretization of an
> elliptic equation. The mesh has 1 million control volumes and there are two
> more constraints for the system.
> >>
> >> First, I've solved it in MATLAB using backslash command, which in turn
> calls CHOLMOD once the matrix is SPD. Using tic and toc funtions, I could
> see that it takes about 2s for the system to be solved (See attached for
> more details).
> >>
> >> I wrote both matrix and rhs in PETSc binary format and solved the
> linear system using the example problem defined in
> ksp/examples/tutorials/ex10.c. The command line options were:
> >>
> >> mpiexec -n -1 ./ex10 -f A1mi.dat -rhs rhs1mi.dat -log_summary
> -ksp_monitos -ksp_view -ksp_type preonly -pc_type cholesky
> -pc_factor_mat_solver_package cholmod
> >>
> >> The configuration parameters for CHOLMOD in PETSc and MATLAB seems the
> same, so I was expecting a similar computation time, but it took about 13s
> to solve in PETSc. (See attached for more details).
> >>
> >> Why does CHOLMOD solution time differs between them?
> >>
> >> If someone wants to try for yourself, here are the binaries for the
> matrix and the rhs, respectively.
> >> https://www.dropbox.com/s/q9s6mlrmv1qdxon/A1mi.dat?dl=0
> >> https://www.dropbox.com/s/2zadcbjg5d9bycy/rhs1mi.dat?dl=0
> >>
> >>
> >>
> >> <PetscOutput.dat>
> >> <MatlabOutput.dat>
>
>
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