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<p class="MsoNormal">Dear Jose : <o:p></o:p></p>
<p class="MsoNormal">I came across this thread describing issue using krylovschur and finding eigenvectors non-orthogonal.
<o:p></o:p></p>
<p class="MsoNormal"><a href="https://lists.mcs.anl.gov/pipermail/petsc-users/2014-October/023360.html">https://lists.mcs.anl.gov/pipermail/petsc-users/2014-October/023360.html</a><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I furthermore have tested by reducing the tolerance as highlighted below from 1e-12 to 1e-16 with no luck.
<o:p></o:p></p>
<p class="MsoNormal">Could you please suggest options/sources to try out ? <o:p></o:p></p>
<p class="MsoNormal">Thanks a lot for sharing your knowledge! <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Sincere,<o:p></o:p></p>
<p class="MsoNormal">Kuang-Chung Wang <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">=======================================================<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Kuang-Chung Wang <o:p>
</o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Computational and Modeling Technology<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Intel Corporation<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">Hillsboro OR 97124<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">=======================================================<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Here are more info: <o:p></o:p></p>
<ol style="margin-top:0in" start="1" type="1">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">slepc/3.7.4
<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1">output message from by doing EPSView(eps,PETSC_NULL):
<o:p></o:p></li></ol>
<p class="MsoNormal">EPS Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: krylovschur<o:p></o:p></p>
<p class="MsoNormal"> Krylov-Schur: 50% of basis vectors kept after restart<o:p></o:p></p>
<p class="MsoNormal"> Krylov-Schur: using the locking variant<o:p></o:p></p>
<p class="MsoNormal"> problem type: non-hermitian eigenvalue problem<o:p></o:p></p>
<p class="MsoNormal"> selected portion of the spectrum: closest to target: 20.1161 (in magnitude)<o:p></o:p></p>
<p class="MsoNormal"> number of eigenvalues (nev): 40<o:p></o:p></p>
<p class="MsoNormal"> number of column vectors (ncv): 81<o:p></o:p></p>
<p class="MsoNormal"> maximum dimension of projected problem (mpd): 81<o:p></o:p></p>
<p class="MsoNormal"> maximum number of iterations: 1000<o:p></o:p></p>
<p class="MsoNormal"><span style="color:red"> tolerance: 1e-12<o:p></o:p></span></p>
<p class="MsoNormal"> convergence test: relative to the eigenvalue<o:p></o:p></p>
<p class="MsoNormal">BV Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: svec<o:p></o:p></p>
<p class="MsoNormal"> 82 columns of global length 2988<o:p></o:p></p>
<p class="MsoNormal"> vector orthogonalization method: classical Gram-Schmidt<o:p></o:p></p>
<p class="MsoNormal"> orthogonalization refinement: always<o:p></o:p></p>
<p class="MsoNormal"> block orthogonalization method: Gram-Schmidt<o:p></o:p></p>
<p class="MsoNormal"> doing matmult as a single matrix-matrix product<o:p></o:p></p>
<p class="MsoNormal">DS Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: nhep<o:p></o:p></p>
<p class="MsoNormal">ST Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: sinvert<o:p></o:p></p>
<p class="MsoNormal"> shift: 20.1161<o:p></o:p></p>
<p class="MsoNormal"> number of matrices: 1<o:p></o:p></p>
<p class="MsoNormal"> KSP Object: (st_) 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: preonly<o:p></o:p></p>
<p class="MsoNormal"> maximum iterations=1000, initial guess is zero<o:p></o:p></p>
<p class="MsoNormal"> tolerances: relative=1.12005e-09, absolute=1e-50, divergence=10000.<o:p></o:p></p>
<p class="MsoNormal"> left preconditioning<o:p></o:p></p>
<p class="MsoNormal"> using NONE norm type for convergence test<o:p></o:p></p>
<p class="MsoNormal"> PC Object: (st_) 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: lu<o:p></o:p></p>
<p class="MsoNormal"> LU: out-of-place factorization<o:p></o:p></p>
<p class="MsoNormal"> tolerance for zero pivot 2.22045e-14<o:p></o:p></p>
<p class="MsoNormal"> matrix ordering: nd<o:p></o:p></p>
<p class="MsoNormal"> factor fill ratio given 0., needed 0.<o:p></o:p></p>
<p class="MsoNormal"> Factored matrix follows:<o:p></o:p></p>
<p class="MsoNormal"> Mat Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: seqaij<o:p></o:p></p>
<p class="MsoNormal"> rows=2988, cols=2988<o:p></o:p></p>
<p class="MsoNormal"> package used to perform factorization: mumps<o:p></o:p></p>
<p class="MsoNormal"> total: nonzeros=614160, allocated nonzeros=614160<o:p></o:p></p>
<p class="MsoNormal"> total number of mallocs used during MatSetValues calls =0<o:p></o:p></p>
<p class="MsoNormal"> MUMPS run parameters:<o:p></o:p></p>
<p class="MsoNormal"> SYM (matrix type): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> PAR (host participation): 1 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(1) (output for error): 6 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(2) (output of diagnostic msg): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(3) (output for global info): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(4) (level of printing): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(5) (input mat struct): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(6) (matrix prescaling): 7 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(7) (sequential matrix ordering):7 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(8) (scaling strategy): 77 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(10) (max num of refinements): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(11) (error analysis): 0 <o:p>
</o:p></p>
<p class="MsoNormal"> ICNTL(12) (efficiency control): 1
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(13) (efficiency control): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(14) (percentage of estimated workspace increase): 20
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(18) (input mat struct): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(19) (Schur complement info): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(20) (rhs sparse pattern): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(21) (solution struct): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(22) (in-core/out-of-core facility): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(23) (max size of memory can be allocated locally):0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(24) (detection of null pivot rows): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(25) (computation of a null space basis): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(26) (Schur options for rhs or solution): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(27) (experimental parameter): -24
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(28) (use parallel or sequential ordering): 1
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(29) (parallel ordering): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(30) (user-specified set of entries in inv(A)): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(31) (factors is discarded in the solve phase): 0
<o:p></o:p></p>
<p class="MsoNormal"> ICNTL(33) (compute determinant): 0
<o:p></o:p></p>
<p class="MsoNormal"> CNTL(1) (relative pivoting threshold): 0.01
<o:p></o:p></p>
<p class="MsoNormal"> CNTL(2) (stopping criterion of refinement): 1.49012e-08
<o:p></o:p></p>
<p class="MsoNormal"> CNTL(3) (absolute pivoting threshold): 0.
<o:p></o:p></p>
<p class="MsoNormal"> CNTL(4) (value of static pivoting): -1.
<o:p></o:p></p>
<p class="MsoNormal"> CNTL(5) (fixation for null pivots): 0.
<o:p></o:p></p>
<p class="MsoNormal"> RINFO(1) (local estimated flops for the elimination after analysis):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 8.15668e+07 <o:p></o:p></p>
<p class="MsoNormal"> RINFO(2) (local estimated flops for the assembly after factorization):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 892584. <o:p></o:p></p>
<p class="MsoNormal"> RINFO(3) (local estimated flops for the elimination after factorization):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 8.15668e+07 <o:p></o:p></p>
<p class="MsoNormal"> INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 16 <o:p></o:p></p>
<p class="MsoNormal"> INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 16 <o:p></o:p></p>
<p class="MsoNormal"> INFO(23) (num of pivots eliminated on this processor after factorization):
<o:p></o:p></p>
<p class="MsoNormal"> [0] 2988 <o:p></o:p></p>
<p class="MsoNormal"> RINFOG(1) (global estimated flops for the elimination after analysis): 8.15668e+07
<o:p></o:p></p>
<p class="MsoNormal"> RINFOG(2) (global estimated flops for the assembly after factorization): 892584.
<o:p></o:p></p>
<p class="MsoNormal"> RINFOG(3) (global estimated flops for the elimination after factorization): 8.15668e+07
<o:p></o:p></p>
<p class="MsoNormal"> (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)<o:p></o:p></p>
<p class="MsoNormal"> INFOG(3) (estimated real workspace for factors on all processors after analysis): 614160
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(4) (estimated integer workspace for factors on all processors after analysis): 31971
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(5) (estimated maximum front size in the complete tree): 246
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(6) (number of nodes in the complete tree): 197
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(7) (ordering option effectively use after analysis): 2
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 614160
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(10) (total integer space store the matrix factors after factorization): 31971
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(11) (order of largest frontal matrix after factorization): 246
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(12) (number of off-diagonal pivots): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(13) (number of delayed pivots after factorization): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(14) (number of memory compress after factorization): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(15) (number of steps of iterative refinement after solution): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 16
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 16
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 16
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 16
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(20) (estimated number of entries in the factors): 614160
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 14
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 14
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
<o:p></o:p></p>
<p class="MsoNormal"> INFOG(28) (after factorization: number of null pivots encountered): 0<o:p></o:p></p>
<p class="MsoNormal"> INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 614160<o:p></o:p></p>
<p class="MsoNormal"> INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 13, 13<o:p></o:p></p>
<p class="MsoNormal"> INFOG(32) (after analysis: type of analysis done): 1<o:p></o:p></p>
<p class="MsoNormal"> INFOG(33) (value used for ICNTL(8)): 7<o:p></o:p></p>
<p class="MsoNormal"> INFOG(34) (exponent of the determinant if determinant is requested): 0<o:p></o:p></p>
<p class="MsoNormal"> linear system matrix = precond matrix:<o:p></o:p></p>
<p class="MsoNormal"> Mat Object: 1 MPI processes<o:p></o:p></p>
<p class="MsoNormal"> type: seqaij<o:p></o:p></p>
<p class="MsoNormal"> rows=2988, cols=2988<o:p></o:p></p>
<p class="MsoNormal"> total: nonzeros=151488, allocated nonzeros=151488<o:p></o:p></p>
<p class="MsoNormal"> total number of mallocs used during MatSetValues calls =0<o:p></o:p></p>
<p class="MsoNormal"> using I-node routines: found 996 nodes, limit used is 5<o:p></o:p></p>
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