Dear Jose, Thanks for your reply. The problem I deal with (rotational fluid dynamics) involves a very small parameter, the Ekman number, which needs to be as small as possible, hopefully 10^-10 or smaller (typical of the molten core of a planet). I have noticed (and other authors before) that round-off errors become more noticeable as this Ekman number is made smaller. That is why it would be nice to have some calculations done with quad precision, it will also help to estimate the round-off errors when working with double-precision. As far as I understand MUMPS doesn't do quad precision but all native methods in petsc/slepc can do it. Below is the output of -eps_view for a typical run. Thanks again! Santiago EPS Object: 12 MPI processes type: krylovschur 50% of basis vectors kept after restart using the locking variant problem type: generalized non-hermitian eigenvalue problem balancing enabled: one-sided Krylov, with its=5 selected portion of the spectrum: closest to target: -0.000828692+1.00018i (in magnitude) number of eigenvalues (nev): 2 number of column vectors (ncv): 17 maximum dimension of projected problem (mpd): 17 maximum number of iterations: 160 tolerance: 1e-18 convergence test: relative to the eigenvalue BV Object: 12 MPI processes type: svec 18 columns of global length 903168 vector orthogonalization method: classical Gram-Schmidt orthogonalization refinement: if needed (eta: 0.7071) block orthogonalization method: Gram-Schmidt doing matmult as a single matrix-matrix product DS Object: 12 MPI processes type: nhep parallel operation mode: REDUNDANT ST Object: 12 MPI processes type: sinvert shift: -0.000828692+1.00018i number of matrices: 2 all matrices have different nonzero pattern KSP Object: (st_) 12 MPI processes type: preonly maximum iterations=10000, initial guess is zero tolerances: relative=1e-08, absolute=1e-50, divergence=10000. left preconditioning using NONE norm type for convergence test PC Object: (st_) 12 MPI processes type: lu out-of-place factorization tolerance for zero pivot 2.22045e-14 matrix ordering: natural factor fill ratio given 0., needed 0. Factored matrix follows: Mat Object: 12 MPI processes type: mumps rows=903168, cols=903168 package used to perform factorization: mumps total: nonzeros=357531912, allocated nonzeros=357531912 total number of mallocs used during MatSetValues calls =0 MUMPS run parameters: SYM (matrix type): 0 PAR (host participation): 1 ICNTL(1) (output for error): 6 ICNTL(2) (output of diagnostic msg): 0 ICNTL(3) (output for global info): 0 ICNTL(4) (level of printing): 0 ICNTL(5) (input mat struct): 0 ICNTL(6) (matrix prescaling): 7 ICNTL(7) (sequential matrix ordering):7 ICNTL(8) (scaling strategy): 77 ICNTL(10) (max num of refinements): 0 ICNTL(11) (error analysis): 0 ICNTL(12) (efficiency control): 1 ICNTL(13) (efficiency control): 0 ICNTL(14) (percentage of estimated workspace increase): 30 ICNTL(18) (input mat struct): 3 ICNTL(19) (Schur complement info): 0 ICNTL(20) (rhs sparse pattern): 0 ICNTL(21) (solution struct): 1 ICNTL(22) (in-core/out-of-core facility): 0 ICNTL(23) (max size of memory can be allocated locally):0 ICNTL(24) (detection of null pivot rows): 0 ICNTL(25) (computation of a null space basis): 0 ICNTL(26) (Schur options for rhs or solution): 0 ICNTL(27) (experimental parameter): -32 ICNTL(28) (use parallel or sequential ordering): 1 ICNTL(29) (parallel ordering): 0 ICNTL(30) (user-specified set of entries in inv(A)): 0 ICNTL(31) (factors is discarded in the solve phase): 0 ICNTL(33) (compute determinant): 0 CNTL(1) (relative pivoting threshold): 0.01 CNTL(2) (stopping criterion of refinement): 1.49012e-08 CNTL(3) (absolute pivoting threshold): 0. CNTL(4) (value of static pivoting): -1. CNTL(5) (fixation for null pivots): 0. RINFO(1) (local estimated flops for the elimination after analysis): [0] 3.19646e+10 [1] 2.52681e+10 [2] 2.44386e+10 [3] 1.9843e+10 [4] 1.98101e+10 [5] 1.99033e+10 [6] 2.43184e+10 [7] 1.96892e+10 [8] 1.99212e+10 [9] 2.03623e+10 [10] 3.43984e+10 [11] 3.19496e+10 RINFO(2) (local estimated flops for the assembly after factorization): [0] 6.77645e+07 [1] 7.50768e+07 [2] 6.47743e+07 [3] 4.58456e+07 [4] 4.43134e+07 [5] 4.71606e+07 [6] 4.76135e+07 [7] 4.66102e+07 [8] 4.8116e+07 [9] 4.81349e+07 [10] 8.36226e+07 [11] 7.80849e+07 RINFO(3) (local estimated flops for the elimination after factorization): [0] 3.08628e+10 [1] 2.57087e+10 [2] 2.48956e+10 [3] 2.04365e+10 [4] 2.00618e+10 [5] 2.04788e+10 [6] 2.4473e+10 [7] 1.96377e+10 [8] 1.90936e+10 [9] 2.10852e+10 [10] 3.40174e+10 [11] 3.25389e+10 INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization): [0] 1023 [1] 1072 [2] 928 [3] 736 [4] 736 [5] 770 [6] 810 [7] 739 [8] 783 [9] 761 [10] 1163 [11] 1229 INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization): [0] 1023 [1] 1072 [2] 928 [3] 736 [4] 736 [5] 770 [6] 810 [7] 739 [8] 783 [9] 761 [10] 1163 [11] 1229 INFO(23) (num of pivots eliminated on this processor after factorization): [0] 86694 [1] 110879 [2] 83326 [3] 56448 [4] 55775 [5] 57124 [6] 57115 [7] 56671 [8] 58017 [9] 57345 [10] 111545 [11] 112229 RINFOG(1) (global estimated flops for the elimination after analysis): 2.91867e+11 RINFOG(2) (global estimated flops for the assembly after factorization): 6.97117e+08 RINFOG(3) (global estimated flops for the elimination after factorization): 2.9329e+11 (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0) INFOG(3) (estimated real workspace for factors on all processors after analysis): 357531912 INFOG(4) (estimated integer workspace for factors on all processors after analysis): 11477656 INFOG(5) (estimated maximum front size in the complete tree): 2016 INFOG(6) (number of nodes in the complete tree): 67821 INFOG(7) (ordering option effectively use after analysis): 5 INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 72 INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 358009746 INFOG(10) (total integer space store the matrix factors after factorization): 11469827 INFOG(11) (order of largest frontal matrix after factorization): 2032 INFOG(12) (number of off-diagonal pivots): 12941 INFOG(13) (number of delayed pivots after factorization): 617 INFOG(14) (number of memory compress after factorization): 0 INFOG(15) (number of steps of iterative refinement after solution): 0 INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 1229 INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 10750 INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 1229 INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 10750 INFOG(20) (estimated number of entries in the factors): 357531912 INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 945 INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 8386 INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0 INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1 INFOG(25) (after factorization: number of pivots modified by static pivoting): 0 INFOG(28) (after factorization: number of null pivots encountered): 0 INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 358009746 INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 1105, 9342 INFOG(32) (after analysis: type of analysis done): 1 INFOG(33) (value used for ICNTL(8)): 7 INFOG(34) (exponent of the determinant if determinant is requested): 0 linear system matrix = precond matrix: Mat Object: 12 MPI processes type: mpiaij rows=903168, cols=903168 total: nonzeros=17538393, allocated nonzeros=17538393 total number of mallocs used during MatSetValues calls =0 not using I-node (on process 0) routines On Sun, Mar 4, 2018 at 10:12 PM, Jose E. Roman <[email protected]> wrote:

Why do you want to move to quad precision? Double precision is usually enough. The fact that B is singular should not be a problem, provided that you do shift-and-invert with a nonzero target value. Can you send the output of -eps_view so that I can get a better idea what you are doing?

Jose

...

El 5 mar 2018, a las 0:50, Santiago Andres Triana <[email protected]> escribió:

Dear all,

A rather general question, is there any possibility of solving a complex-valued generalized eigenvalue problem using quad (or extended) precision when the 'B' matrix is singular? So far I have been using MUMPS with double precision with good results but I require eventually extended precision. Any comment or advice highly welcome. Thanks in advance!

Santiago