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Hi Kuang-Chung Wang ,<br>
<br>
It says your eigenvalue problem type is: <br>
problem type: non-hermitian eigenvalue problem<br>
<br>
While the email chain you refer to is for a hermitian eigenvalue problem. <br>
Try changing your eigenvalue problem type to a hermitian or generalized hermitian problem and it should produce orthogonal eigenvectors.<br>
<br>
Lucas<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> petsc-users <petsc-users-bounces@mcs.anl.gov> on behalf of Wang, Kuang-chung <kuang-chung.wang@intel.com><br>
<b>Sent:</b> Wednesday, November 24, 2021 12:15 AM<br>
<b>To:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Cc:</b> Obradovic, Borna <borna.obradovic@intel.com>; Cea, Stephen M <stephen.m.cea@intel.com><br>
<b>Subject:</b> Re: [petsc-users] Orthogonality of eigenvectors in SLEPC</font>
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<p class="x_MsoNormal">Dear Jose : </p>
<p class="x_MsoNormal">I came across this thread describing issue using krylovschur and finding eigenvectors non-orthogonal.
</p>
<p class="x_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></p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal">I furthermore have tested by reducing the tolerance as highlighted below from 1e-12 to 1e-16 with no luck.
</p>
<p class="x_MsoNormal">Could you please suggest options/sources to try out ? </p>
<p class="x_MsoNormal">Thanks a lot for sharing your knowledge! </p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal">Sincere,</p>
<p class="x_MsoNormal">Kuang-Chung Wang </p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">=======================================================</span></p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">Kuang-Chung Wang </span>
</p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">Computational and Modeling Technology</span></p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">Intel Corporation</span></p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">Hillsboro OR 97124</span></p>
<p class="x_MsoNormal"><span style="font-family:"Courier New"">=======================================================</span></p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal">Here are more info: </p>
<ol start="1" type="1" style="margin-top:0in">
<li class="x_MsoListParagraph" style="margin-left:0in">slepc/3.7.4 </li><li class="x_MsoListParagraph" style="margin-left:0in">output message from by doing EPSView(eps,PETSC_NULL):
</li></ol>
<p class="x_MsoNormal">EPS Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: krylovschur</p>
<p class="x_MsoNormal"> Krylov-Schur: 50% of basis vectors kept after restart</p>
<p class="x_MsoNormal"> Krylov-Schur: using the locking variant</p>
<p class="x_MsoNormal"> problem type: non-hermitian eigenvalue problem</p>
<p class="x_MsoNormal"> selected portion of the spectrum: closest to target: 20.1161 (in magnitude)</p>
<p class="x_MsoNormal"> number of eigenvalues (nev): 40</p>
<p class="x_MsoNormal"> number of column vectors (ncv): 81</p>
<p class="x_MsoNormal"> maximum dimension of projected problem (mpd): 81</p>
<p class="x_MsoNormal"> maximum number of iterations: 1000</p>
<p class="x_MsoNormal"><span style="color:red"> tolerance: 1e-12</span></p>
<p class="x_MsoNormal"> convergence test: relative to the eigenvalue</p>
<p class="x_MsoNormal">BV Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: svec</p>
<p class="x_MsoNormal"> 82 columns of global length 2988</p>
<p class="x_MsoNormal"> vector orthogonalization method: classical Gram-Schmidt</p>
<p class="x_MsoNormal"> orthogonalization refinement: always</p>
<p class="x_MsoNormal"> block orthogonalization method: Gram-Schmidt</p>
<p class="x_MsoNormal"> doing matmult as a single matrix-matrix product</p>
<p class="x_MsoNormal">DS Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: nhep</p>
<p class="x_MsoNormal">ST Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: sinvert</p>
<p class="x_MsoNormal"> shift: 20.1161</p>
<p class="x_MsoNormal"> number of matrices: 1</p>
<p class="x_MsoNormal"> KSP Object: (st_) 1 MPI processes</p>
<p class="x_MsoNormal"> type: preonly</p>
<p class="x_MsoNormal"> maximum iterations=1000, initial guess is zero</p>
<p class="x_MsoNormal"> tolerances: relative=1.12005e-09, absolute=1e-50, divergence=10000.</p>
<p class="x_MsoNormal"> left preconditioning</p>
<p class="x_MsoNormal"> using NONE norm type for convergence test</p>
<p class="x_MsoNormal"> PC Object: (st_) 1 MPI processes</p>
<p class="x_MsoNormal"> type: lu</p>
<p class="x_MsoNormal"> LU: out-of-place factorization</p>
<p class="x_MsoNormal"> tolerance for zero pivot 2.22045e-14</p>
<p class="x_MsoNormal"> matrix ordering: nd</p>
<p class="x_MsoNormal"> factor fill ratio given 0., needed 0.</p>
<p class="x_MsoNormal"> Factored matrix follows:</p>
<p class="x_MsoNormal"> Mat Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: seqaij</p>
<p class="x_MsoNormal"> rows=2988, cols=2988</p>
<p class="x_MsoNormal"> package used to perform factorization: mumps</p>
<p class="x_MsoNormal"> total: nonzeros=614160, allocated nonzeros=614160</p>
<p class="x_MsoNormal"> total number of mallocs used during MatSetValues calls =0</p>
<p class="x_MsoNormal"> MUMPS run parameters:</p>
<p class="x_MsoNormal"> SYM (matrix type): 0 </p>
<p class="x_MsoNormal"> PAR (host participation): 1 </p>
<p class="x_MsoNormal"> ICNTL(1) (output for error): 6 </p>
<p class="x_MsoNormal"> ICNTL(2) (output of diagnostic msg): 0 </p>
<p class="x_MsoNormal"> ICNTL(3) (output for global info): 0 </p>
<p class="x_MsoNormal"> ICNTL(4) (level of printing): 0 </p>
<p class="x_MsoNormal"> ICNTL(5) (input mat struct): 0 </p>
<p class="x_MsoNormal"> ICNTL(6) (matrix prescaling): 7 </p>
<p class="x_MsoNormal"> ICNTL(7) (sequential matrix ordering):7 </p>
<p class="x_MsoNormal"> ICNTL(8) (scaling strategy): 77 </p>
<p class="x_MsoNormal"> ICNTL(10) (max num of refinements): 0 </p>
<p class="x_MsoNormal"> ICNTL(11) (error analysis): 0 </p>
<p class="x_MsoNormal"> ICNTL(12) (efficiency control): 1
</p>
<p class="x_MsoNormal"> ICNTL(13) (efficiency control): 0
</p>
<p class="x_MsoNormal"> ICNTL(14) (percentage of estimated workspace increase): 20
</p>
<p class="x_MsoNormal"> ICNTL(18) (input mat struct): 0
</p>
<p class="x_MsoNormal"> ICNTL(19) (Schur complement info): 0
</p>
<p class="x_MsoNormal"> ICNTL(20) (rhs sparse pattern): 0
</p>
<p class="x_MsoNormal"> ICNTL(21) (solution struct): 0
</p>
<p class="x_MsoNormal"> ICNTL(22) (in-core/out-of-core facility): 0
</p>
<p class="x_MsoNormal"> ICNTL(23) (max size of memory can be allocated locally):0
</p>
<p class="x_MsoNormal"> ICNTL(24) (detection of null pivot rows): 0
</p>
<p class="x_MsoNormal"> ICNTL(25) (computation of a null space basis): 0
</p>
<p class="x_MsoNormal"> ICNTL(26) (Schur options for rhs or solution): 0
</p>
<p class="x_MsoNormal"> ICNTL(27) (experimental parameter): -24
</p>
<p class="x_MsoNormal"> ICNTL(28) (use parallel or sequential ordering): 1
</p>
<p class="x_MsoNormal"> ICNTL(29) (parallel ordering): 0
</p>
<p class="x_MsoNormal"> ICNTL(30) (user-specified set of entries in inv(A)): 0
</p>
<p class="x_MsoNormal"> ICNTL(31) (factors is discarded in the solve phase): 0
</p>
<p class="x_MsoNormal"> ICNTL(33) (compute determinant): 0
</p>
<p class="x_MsoNormal"> CNTL(1) (relative pivoting threshold): 0.01
</p>
<p class="x_MsoNormal"> CNTL(2) (stopping criterion of refinement): 1.49012e-08
</p>
<p class="x_MsoNormal"> CNTL(3) (absolute pivoting threshold): 0.
</p>
<p class="x_MsoNormal"> CNTL(4) (value of static pivoting): -1.
</p>
<p class="x_MsoNormal"> CNTL(5) (fixation for null pivots): 0.
</p>
<p class="x_MsoNormal"> RINFO(1) (local estimated flops for the elimination after analysis):
</p>
<p class="x_MsoNormal"> [0] 8.15668e+07 </p>
<p class="x_MsoNormal"> RINFO(2) (local estimated flops for the assembly after factorization):
</p>
<p class="x_MsoNormal"> [0] 892584. </p>
<p class="x_MsoNormal"> RINFO(3) (local estimated flops for the elimination after factorization):
</p>
<p class="x_MsoNormal"> [0] 8.15668e+07 </p>
<p class="x_MsoNormal"> INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
</p>
<p class="x_MsoNormal"> [0] 16 </p>
<p class="x_MsoNormal"> INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
</p>
<p class="x_MsoNormal"> [0] 16 </p>
<p class="x_MsoNormal"> INFO(23) (num of pivots eliminated on this processor after factorization):
</p>
<p class="x_MsoNormal"> [0] 2988 </p>
<p class="x_MsoNormal"> RINFOG(1) (global estimated flops for the elimination after analysis): 8.15668e+07
</p>
<p class="x_MsoNormal"> RINFOG(2) (global estimated flops for the assembly after factorization): 892584.
</p>
<p class="x_MsoNormal"> RINFOG(3) (global estimated flops for the elimination after factorization): 8.15668e+07
</p>
<p class="x_MsoNormal"> (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)</p>
<p class="x_MsoNormal"> INFOG(3) (estimated real workspace for factors on all processors after analysis): 614160
</p>
<p class="x_MsoNormal"> INFOG(4) (estimated integer workspace for factors on all processors after analysis): 31971
</p>
<p class="x_MsoNormal"> INFOG(5) (estimated maximum front size in the complete tree): 246
</p>
<p class="x_MsoNormal"> INFOG(6) (number of nodes in the complete tree): 197
</p>
<p class="x_MsoNormal"> INFOG(7) (ordering option effectively use after analysis): 2
</p>
<p class="x_MsoNormal"> INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
</p>
<p class="x_MsoNormal"> INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 614160
</p>
<p class="x_MsoNormal"> INFOG(10) (total integer space store the matrix factors after factorization): 31971
</p>
<p class="x_MsoNormal"> INFOG(11) (order of largest frontal matrix after factorization): 246
</p>
<p class="x_MsoNormal"> INFOG(12) (number of off-diagonal pivots): 0
</p>
<p class="x_MsoNormal"> INFOG(13) (number of delayed pivots after factorization): 0
</p>
<p class="x_MsoNormal"> INFOG(14) (number of memory compress after factorization): 0
</p>
<p class="x_MsoNormal"> INFOG(15) (number of steps of iterative refinement after solution): 0
</p>
<p class="x_MsoNormal"> INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 16
</p>
<p class="x_MsoNormal"> INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 16
</p>
<p class="x_MsoNormal"> INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 16
</p>
<p class="x_MsoNormal"> INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 16
</p>
<p class="x_MsoNormal"> INFOG(20) (estimated number of entries in the factors): 614160
</p>
<p class="x_MsoNormal"> INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 14
</p>
<p class="x_MsoNormal"> INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 14
</p>
<p class="x_MsoNormal"> INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
</p>
<p class="x_MsoNormal"> INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
</p>
<p class="x_MsoNormal"> INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
</p>
<p class="x_MsoNormal"> INFOG(28) (after factorization: number of null pivots encountered): 0</p>
<p class="x_MsoNormal"> INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 614160</p>
<p class="x_MsoNormal"> INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 13, 13</p>
<p class="x_MsoNormal"> INFOG(32) (after analysis: type of analysis done): 1</p>
<p class="x_MsoNormal"> INFOG(33) (value used for ICNTL(8)): 7</p>
<p class="x_MsoNormal"> INFOG(34) (exponent of the determinant if determinant is requested): 0</p>
<p class="x_MsoNormal"> linear system matrix = precond matrix:</p>
<p class="x_MsoNormal"> Mat Object: 1 MPI processes</p>
<p class="x_MsoNormal"> type: seqaij</p>
<p class="x_MsoNormal"> rows=2988, cols=2988</p>
<p class="x_MsoNormal"> total: nonzeros=151488, allocated nonzeros=151488</p>
<p class="x_MsoNormal"> total number of mallocs used during MatSetValues calls =0</p>
<p class="x_MsoNormal"> using I-node routines: found 996 nodes, limit used is 5</p>
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