Good afternoon,

I am solving generalized eigenvalue problems {Ax = omegaBx} in complex arithmetic, where A is non-hermitian and B is singular. I think the only way to get round the singularity is to employ a shift-and-invert method, where I am using MUMPS to invert the shifted matrix.

I am using the Fortran interface of PETSc 3.8.3 and SLEPc 3.8.2 where my ./configure line was ./configure --with-fortran-kernels=1 --with-scalar-type=complex --with-blaslapack-dir=/home/linuxbrew/.linuxbrew/opt/openblas --PETSC_ARCH=cplx_dble_optim --with-cmake-dir=/home/linuxbrew/.linuxbrew/opt/cmake --with-mpi-dir=/home/linuxbrew/.linuxbrew/opt/openmpi --with-debugging=0 --download-scalapack --download-mumps --COPTFLAGS="-O3 -march=native" --CXXOPTFLAGS="-O3 -march=native" --FOPTFLAGS="-O3 -march=native"

My matrices A and B are assembled correctly in parallel and my preallocation is quasi-optimal in the sense that I don't have any called to mallocs but I may overestimate the required memory for some rows of the matrices. Here is how I setup the EPS problem and solve:

    CALL EPSSetProblemType(eps,EPS_GNHEP,ierr)
    CALL EPSSetOperators(eps,MatA,MatB,ierr)
    CALL EPSSetDimensions(eps,nev,ncv,PETSC_DECIDE,ierr)
    CALL EPSSetTolerances(eps,tol_ev,PETSC_DECIDE,ierr)

    CALL EPSSetFromOptions(eps,ierr)
    CALL EPSSetTarget(eps,shift,ierr)
    CALL EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE,ierr)

    CALL EPSGetST(eps,st,ierr)
    CALL STGetKSP(st,ksp,ierr)
    CALL KSPGetPC(ksp,pc,ierr)

    CALL STSetType(st,STSINVERT,ierr)
    CALL KSPSetType(ksp,KSPPREONLY,ierr)
    CALL PCSetType(pc,PCLU,ierr)

    CALL PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS,ierr)
    CALL PCSetFromOptions(pc,ierr)

    CALL EPSSolve(eps,ierr)
    CALL EPSGetIterationNumber(eps,iter,ierr)
    CALL EPSGetConverged(eps,nev_conv,ierr)

    - Using one MPI process, it takes 1 hour and 22 minutes to retrieve 250 eigenvalues with a Krylov subspace of size 500, a tolerance of 10^-12 when the leading dimension of the matrices is 405000. My matrix A has 98,415,000 non-zero elements and B has 1,215,000 non zero elements. Would you be shocked by that computation time? I would have expected something much lower given the values of nev and ncv I have but could be completely wrong in my understanding of the Krylov-Schur method.

    - My goal is speed and reliability. Is there anything you notice in my EPS solver that could be improved or corrected? I remember an exchange with Jose E. Roman where he said that the parameters of MUMPS are not worth being changed, however I notice some people play with the -mat_mumps_cntl_1 and  -mat_mumps_cntl_3 which control the relative/absolute pivoting threshold?

    - Would you advise the use of EPSSetTrueResidual and EPSSetBalance since I am using a spectral transformation?

    - Would you see anything that would prevent me from getting speedup in parallel executions?

Thank you very much in advance and I look forward to exchanging with you about these different points,


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