[petsc-users] Krylov-Schur Tolerance
Christopher Pierce
cmpierce at WPI.EDU
Sun Feb 19 04:00:41 CST 2017
Thanks,
Those changes did improve the tolerances of the solutions. However, I
still have the same problem. For certain matrices the error is up to
10^4 times as large as the requested tolerances and when using true
residual the solver gets stuck on a certain residual norm the solutions
and does not converge. I dumped the settings that I used which I'm
attaching here.
Chris
On 02/17/17 04:42, Jose E. Roman wrote:
> For computing eigenvalues with smallest real part of generalized problems Ax=lambda Bx, it may be better to use a target value (instead of -eps_smallest_real). For instance, if you know that all eigenvalues are positive, use -eps_target 0 -eps_target_magnitude
>
> What linear solvers are you using? In the default setting, the coefficient matrix for linear solves will be B, but with target=sigma the coefficient matrix will be A-sigma*B; this may make a difference. Also, in any case, if experiencing convergence problems I would suggest using MUMPS (see section 3.4.1 of SLEPc's users manual).
>
> Jose
>
>
>
>> El 17 feb 2017, a las 10:25, Christopher Pierce <cmpierce at WPI.EDU> escribió:
>>
>> Hello All,
>>
>> I'm trying to use the SLEPc Krylov-Schur implementation to solve a
>> general eigenvalue problem. I have a monitor on my solver and the
>> solutions appear to converge correctly when using the approximation for
>> the residual norm in the algorithm. However, when the solutions are
>> displayed and I retrieve the actual residual norm it is very large and
>> increases with the size of the matrices I am working with. In some
>> cases it may be 10^17 times as large as the approximate norm. I also
>> don't get the eigenvalues I would expect for the system I am studying.
>>
>> When I turn on the option "true residual" the solver fails to converge.
>> The residual norm shrinks to some limit (~10^-3) and then sits there for
>> the remaining iterations. As a note, I am solving for the eigenvalues
>> with the smallest real part. I have also tried the RQCG solver on the
>> same problems and appear to get the correct results using it, but I'm
>> looking to use the better scaling of the Krylov-Schur solver.
>>
>> Does anyone know what could be causing this behavior?
>>
>> Thanks,
>>
>> Chris Pierce
>> WPI Center for Computational Nanoscience
>>
>>
-------------- next part --------------
EPS Object: 4 MPI processes
type: krylovschur
Krylov-Schur: 50% of basis vectors kept after restart
Krylov-Schur: using the locking variant
problem type: generalized symmetric eigenvalue problem
selected portion of the spectrum: closest to target: 0. (in magnitude)
postprocessing eigenvectors with purification
number of eigenvalues (nev): 10
number of column vectors (ncv): 25
maximum dimension of projected problem (mpd): 25
maximum number of iterations: 1000
tolerance: 1e-10
convergence test: relative to the eigenvalue
BV Object: 4 MPI processes
type: svec
26 columns of global length 12513
vector orthogonalization method: classical Gram-Schmidt
orthogonalization refinement: if needed (eta: 0.7071)
block orthogonalization method: Gram-Schmidt
non-standard inner product
Mat Object: 4 MPI processes
type: mpiaij
rows=12513, cols=12513
total: nonzeros=177931, allocated nonzeros=177931
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
doing matmult as a single matrix-matrix product
DS Object: 4 MPI processes
type: hep
solving the problem with: Implicit QR method (_steqr)
ST Object: 4 MPI processes
type: sinvert
shift: 0.
number of matrices: 2
all matrices have different nonzero pattern
KSP Object: (st_) 4 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_) 4 MPI processes
type: lu
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: 4 MPI processes
type: mpiaij
rows=12513, cols=12513
package used to perform factorization: mumps
total: nonzeros=4234311, allocated nonzeros=4234311
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) (sequentia matrix ordering):7
ICNTL(8) (scalling 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): 20
ICNTL(18) (input mat struct): 3
ICNTL(19) (Shur 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): -24
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] 3.42689e+08
[1] 5.94214e+08
[2] 3.8211e+08
[3] 3.4841e+08
RINFO(2) (local estimated flops for the assembly after factorization):
[0] 1.5205e+06
[1] 1.4933e+06
[2] 1.4988e+06
[3] 1.56079e+06
RINFO(3) (local estimated flops for the elimination after factorization):
[0] 3.42689e+08
[1] 5.94214e+08
[2] 3.8211e+08
[3] 3.4841e+08
INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
[0] 37
[1] 44
[2] 40
[3] 38
INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
[0] 37
[1] 44
[2] 40
[3] 38
INFO(23) (num of pivots eliminated on this processor after factorization):
[0] 3977
[1] 2646
[2] 2409
[3] 3481
RINFOG(1) (global estimated flops for the elimination after analysis): 1.66742e+09
RINFOG(2) (global estimated flops for the assembly after factorization): 6.0734e+06
RINFOG(3) (global estimated flops for the elimination after factorization): 1.66742e+09
(RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)
INFOG(3) (estimated real workspace for factors on all processors after analysis): 4234311
INFOG(4) (estimated integer workspace for factors on all processors after analysis): 169823
INFOG(5) (estimated maximum front size in the complete tree): 925
INFOG(6) (number of nodes in the complete tree): 2357
INFOG(7) (ordering option effectively use after analysis): 4
INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 4234311
INFOG(10) (total integer space store the matrix factors after factorization): 169823
INFOG(11) (order of largest frontal matrix after factorization): 925
INFOG(12) (number of off-diagonal pivots): 0
INFOG(13) (number of delayed pivots after factorization): 0
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): 44
INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 159
INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 44
INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 159
INFOG(20) (estimated number of entries in the factors): 4234311
INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 38
INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 142
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)): 4234311
INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 22, 68
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: 4 MPI processes
type: mpiaij
rows=12513, cols=12513
total: nonzeros=177931, allocated nonzeros=177931
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
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