<div dir="ltr">Dear Jose,<div><br></div><div>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.</div><div><br></div><div>As far as I understand MUMPS doesn't do quad precision but all native methods in petsc/slepc can do it.</div><div><br></div><div>Below is the output of -eps_view for a typical run. Thanks again!</div><div><br></div><div>Santiago</div><div><br></div><div><br></div><div><div>EPS Object: 12 MPI processes</div><div> type: krylovschur</div><div> 50% of basis vectors kept after restart</div><div> using the locking variant</div><div> problem type: generalized non-hermitian eigenvalue problem</div><div> balancing enabled: one-sided Krylov, with its=5</div><div> selected portion of the spectrum: closest to target: -0.000828692+1.00018i (in magnitude)</div><div> number of eigenvalues (nev): 2</div><div> number of column vectors (ncv): 17</div><div> maximum dimension of projected problem (mpd): 17</div><div> maximum number of iterations: 160</div><div> tolerance: 1e-18</div><div> convergence test: relative to the eigenvalue</div><div>BV Object: 12 MPI processes</div><div> type: svec</div><div> 18 columns of global length 903168</div><div> vector orthogonalization method: classical Gram-Schmidt</div><div> orthogonalization refinement: if needed (eta: 0.7071)</div><div> block orthogonalization method: Gram-Schmidt</div><div> doing matmult as a single matrix-matrix product</div><div>DS Object: 12 MPI processes</div><div> type: nhep</div><div> parallel operation mode: REDUNDANT</div><div>ST Object: 12 MPI processes</div><div> type: sinvert</div><div> shift: -0.000828692+1.00018i</div><div> number of matrices: 2</div><div> all matrices have different nonzero pattern</div><div> KSP Object: (st_) 12 MPI processes</div><div> type: preonly</div><div> maximum iterations=10000, initial guess is zero</div><div> tolerances: relative=1e-08, absolute=1e-50, divergence=10000.</div><div> left preconditioning</div><div> using NONE norm type for convergence test</div><div> PC Object: (st_) 12 MPI processes</div><div> type: lu</div><div> out-of-place factorization</div><div> tolerance for zero pivot 2.22045e-14</div><div> matrix ordering: natural</div><div> factor fill ratio given 0., needed 0.</div><div> Factored matrix follows:</div><div> Mat Object: 12 MPI processes</div><div> type: mumps</div><div> rows=903168, cols=903168</div><div> package used to perform factorization: mumps</div><div> total: nonzeros=357531912, allocated nonzeros=357531912</div><div> total number of mallocs used during MatSetValues calls =0</div><div> MUMPS run parameters:</div><div> SYM (matrix type): 0 </div><div> PAR (host participation): 1 </div><div> ICNTL(1) (output for error): 6 </div><div> ICNTL(2) (output of diagnostic msg): 0 </div><div> ICNTL(3) (output for global info): 0 </div><div> ICNTL(4) (level of printing): 0 </div><div> ICNTL(5) (input mat struct): 0 </div><div> ICNTL(6) (matrix prescaling): 7 </div><div> ICNTL(7) (sequential matrix ordering):7 </div><div> ICNTL(8) (scaling strategy): 77 </div><div> ICNTL(10) (max num of refinements): 0 </div><div> ICNTL(11) (error analysis): 0 </div><div> ICNTL(12) (efficiency control): 1 </div><div> ICNTL(13) (efficiency control): 0 </div><div> ICNTL(14) (percentage of estimated workspace increase): 30 </div><div> ICNTL(18) (input mat struct): 3 </div><div> ICNTL(19) (Schur complement info): 0 </div><div> ICNTL(20) (rhs sparse pattern): 0 </div><div> ICNTL(21) (solution struct): 1 </div><div> ICNTL(22) (in-core/out-of-core facility): 0 </div><div> ICNTL(23) (max size of memory can be allocated locally):0 </div><div> ICNTL(24) (detection of null pivot rows): 0 </div><div> ICNTL(25) (computation of a null space basis): 0 </div><div> ICNTL(26) (Schur options for rhs or solution): 0 </div><div> ICNTL(27) (experimental parameter): -32 </div><div> ICNTL(28) (use parallel or sequential ordering): 1 </div><div> ICNTL(29) (parallel ordering): 0 </div><div> ICNTL(30) (user-specified set of entries in inv(A)): 0 </div><div> ICNTL(31) (factors is discarded in the solve phase): 0 </div><div> ICNTL(33) (compute determinant): 0 </div><div> CNTL(1) (relative pivoting threshold): 0.01 </div><div> CNTL(2) (stopping criterion of refinement): 1.49012e-08 </div><div> CNTL(3) (absolute pivoting threshold): 0. </div><div> CNTL(4) (value of static pivoting): -1. </div><div> CNTL(5) (fixation for null pivots): 0. </div><div> RINFO(1) (local estimated flops for the elimination after analysis): </div><div> [0] 3.19646e+10 </div><div> [1] 2.52681e+10 </div><div> [2] 2.44386e+10 </div><div> [3] 1.9843e+10 </div><div> [4] 1.98101e+10 </div><div> [5] 1.99033e+10 </div><div> [6] 2.43184e+10 </div><div> [7] 1.96892e+10 </div><div> [8] 1.99212e+10 </div><div> [9] 2.03623e+10 </div><div> [10] 3.43984e+10 </div><div> [11] 3.19496e+10 </div><div> RINFO(2) (local estimated flops for the assembly after factorization): </div><div> [0] 6.77645e+07 </div><div> [1] 7.50768e+07 </div><div> [2] 6.47743e+07 </div><div> [3] 4.58456e+07 </div><div> [4] 4.43134e+07 </div><div> [5] 4.71606e+07 </div><div> [6] 4.76135e+07 </div><div> [7] 4.66102e+07 </div><div> [8] 4.8116e+07 </div><div> [9] 4.81349e+07 </div><div> [10] 8.36226e+07 </div><div> [11] 7.80849e+07 </div><div> RINFO(3) (local estimated flops for the elimination after factorization): </div><div> [0] 3.08628e+10 </div><div> [1] 2.57087e+10 </div><div> [2] 2.48956e+10 </div><div> [3] 2.04365e+10 </div><div> [4] 2.00618e+10 </div><div> [5] 2.04788e+10 </div><div> [6] 2.4473e+10 </div><div> [7] 1.96377e+10 </div><div> [8] 1.90936e+10 </div><div> [9] 2.10852e+10 </div><div> [10] 3.40174e+10 </div><div> [11] 3.25389e+10 </div><div> INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization): </div><div> [0] 1023 </div><div> [1] 1072 </div><div> [2] 928 </div><div> [3] 736 </div><div> [4] 736 </div><div> [5] 770 </div><div> [6] 810 </div><div> [7] 739 </div><div> [8] 783 </div><div> [9] 761 </div><div> [10] 1163 </div><div> [11] 1229 </div><div> INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization): </div><div> [0] 1023 </div><div> [1] 1072 </div><div> [2] 928 </div><div> [3] 736 </div><div> [4] 736 </div><div> [5] 770 </div><div> [6] 810 </div><div> [7] 739 </div><div> [8] 783 </div><div> [9] 761 </div><div> [10] 1163 </div><div> [11] 1229 </div><div> INFO(23) (num of pivots eliminated on this processor after factorization): </div><div> [0] 86694 </div><div> [1] 110879 </div><div> [2] 83326 </div><div> [3] 56448 </div><div> [4] 55775 </div><div> [5] 57124 </div><div> [6] 57115 </div><div> [7] 56671 </div><div> [8] 58017 </div><div> [9] 57345 </div><div> [10] 111545 </div><div> [11] 112229 </div><div> RINFOG(1) (global estimated flops for the elimination after analysis): 2.91867e+11 </div><div> RINFOG(2) (global estimated flops for the assembly after factorization): 6.97117e+08 </div><div> RINFOG(3) (global estimated flops for the elimination after factorization): 2.9329e+11 </div><div> (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)</div><div> INFOG(3) (estimated real workspace for factors on all processors after analysis): 357531912 </div><div> INFOG(4) (estimated integer workspace for factors on all processors after analysis): 11477656 </div><div> INFOG(5) (estimated maximum front size in the complete tree): 2016 </div><div> INFOG(6) (number of nodes in the complete tree): 67821 </div><div> INFOG(7) (ordering option effectively use after analysis): 5 </div><div> INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 72 </div><div> INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 358009746 </div><div> INFOG(10) (total integer space store the matrix factors after factorization): 11469827 </div><div> INFOG(11) (order of largest frontal matrix after factorization): 2032 </div><div> INFOG(12) (number of off-diagonal pivots): 12941 </div><div> INFOG(13) (number of delayed pivots after factorization): 617 </div><div> INFOG(14) (number of memory compress after factorization): 0 </div><div> INFOG(15) (number of steps of iterative refinement after solution): 0 </div><div> INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 1229 </div><div> INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 10750 </div><div> INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 1229 </div><div> INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 10750 </div><div> INFOG(20) (estimated number of entries in the factors): 357531912 </div><div> INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 945 </div><div> INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 8386 </div><div> INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0 </div><div> INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1 </div><div> INFOG(25) (after factorization: number of pivots modified by static pivoting): 0 </div><div> INFOG(28) (after factorization: number of null pivots encountered): 0</div><div> INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 358009746</div><div> INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 1105, 9342</div><div> INFOG(32) (after analysis: type of analysis done): 1</div><div> INFOG(33) (value used for ICNTL(8)): 7</div><div> INFOG(34) (exponent of the determinant if determinant is requested): 0</div><div> linear system matrix = precond matrix:</div><div> Mat Object: 12 MPI processes</div><div> type: mpiaij</div><div> rows=903168, cols=903168</div><div> total: nonzeros=17538393, allocated nonzeros=17538393</div><div> total number of mallocs used during MatSetValues calls =0</div><div> not using I-node (on process 0) routines</div></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Mar 4, 2018 at 10:12 PM, Jose E. Roman <span dir="ltr"><<a href="mailto:jroman@dsic.upv.es" target="_blank">jroman@dsic.upv.es</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Why do you want to move to quad precision? Double precision is usually enough.<br>
The fact that B is singular should not be a problem, provided that you do shift-and-invert with a nonzero target value.<br>
Can you send the output of -eps_view so that I can get a better idea what you are doing?<br>
<span class="HOEnZb"><font color="#888888"><br>
Jose<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
<br>
> El 5 mar 2018, a las 0:50, Santiago Andres Triana <<a href="mailto:repepo@gmail.com">repepo@gmail.com</a>> escribió:<br>
><br>
> Dear all,<br>
><br>
> 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!<br>
><br>
> Santiago<br>
<br>
</div></div></blockquote></div><br></div>