# [Trilinos-Users] [EXTERNAL] Anasazi BlockKrylovSchur solver Error in F^H M F == I

Klinvex, Alicia Marie amklinv at sandia.gov
Thu Sep 14 08:06:10 EDT 2017

Hello Andris,

I’m sorry to hear you’re having trouble with Anasazi.  The “error” you’re getting isn’t an error in the programming sense.  It’s an error in the mathematical sense.  You turned on debugging output, so it’s printing information that’s useful to the developers.  That message is telling us that F^H M F is approximately equal to I in that the error F^H M F - I is small.

Can you tell us about the linear solver you’re using?  What are the tolerance and maximum number of iterations?  Also, is M a preconditioner, or is M part of the generalized eigenvalue problem Ax = \lambda M x?

Best wishes,
Alicia

From: Trilinos-Users [mailto:trilinos-users-bounces at trilinos.org] On Behalf Of Andris Freimanis
Sent: Thursday, September 14, 2017 1:18 AM
To: Trilinos mailing list <trilinos-users at trilinos.org>
Subject: [EXTERNAL] [Trilinos-Users] Anasazi BlockKrylovSchur solver Error in F^H M F == I

Hello,

I'm trying to calculate few smallest eigenvalues of a linear system, where A - nonsymmetric sparse and M - sparse symmetric positive-definite, using Anasazi's Block Krylov Schur solver with shift-invert transformation that is solved by Belos's block GMRES solver. Both test matrices are  240x240 in size.

Unfortunately, I'm getting this error:   >> Error in F^H M F == I  : 4.44e-16 (copied the full error message below), and can't find info on this in neither Anasazi nor Belos examples or documentation. Can you please take a look at the error message below?

This problem is similar to the one here: https://trilinos.org/pipermail/trilinos-users/2015-December/005270.html. However, the suggestion to use shift-invert doesn't help as I'm already doing that.

Best regards,

Andris Freimanis

Debugging checks: iteration 0: after initialize()
>> Error in F^H M F == I  : 4.44e-16

================================================================================

BlockKrylovSchur Solver Status

The solver is initialized.
The number of iterations performed is 0
The block size is         1
The number of blocks is   24
The current basis size is 0
The number of auxiliary vectors is 0
The number of operations Op*x   is 0

CURRENT RITZ VALUES
[ NONE COMPUTED ]

================================================================================

- StatusTestOutput: Failed
(Num calls,Mod test,State test): (1, 1, Passed Failed Undefined )
- StatusTestCombo: Failed
- StatusTestWithOrdering: Undefined
Quorum: 5
Auxiliary values: [empty]
- StatusTestResNorm: Failed
(Tolerance,WhichNorm,Scaled,Quorum): (1.000000e-03,RITZRES_2NORM,true,5)
Which vectors: [empty]
Performing restart number 1 of 10

Performing restart number 2 of 10

Performing restart number 3 of 10

Performing restart number 4 of 10

Performing restart number 5 of 10

Performing restart number 6 of 10

Performing restart number 7 of 10

Performing restart number 8 of 10

Performing restart number 9 of 10

Performing restart number 10 of 10

Failed.......OR Combination ->
OK...........Number of Iterations = 264 < 1000
Unconverged..(2-Norm Res Vec) / (2-Norm Prec Res0)
residual [ 0 ] = 2.855202e-01 > 1.000000e-03

================================================================================

TimeMonitor results over 1 processor

Timer Name                                           Global time (num calls)
--------------------------------------------------------------------------------
Anasazi: BlockKrylovSchur::Computing Ritz vectors    0 (0)
Anasazi: BlockKrylovSchur::Computing Schur form      0 (0)
Anasazi: BlockKrylovSchur::Operation Op*x            0 (1)
Anasazi: BlockKrylovSchur::Orthogonalization         0.0001295 (1)
Anasazi: BlockKrylovSchur::Sorting Ritz values       0 (0)
Anasazi: BlockKrylovSchur::Sorting Schur form        0 (0)
Anasazi: BlockKrylovSchurSolMgr restarting           0 (0)
Anasazi: BlockKrylovSchurSolMgr::solve()             0 (1)
Belos: BlockGmresSolMgr total solve time             0.03066 (1)
Belos: Operation Op*x                                0.005605 (275)
--------------------------------------------------------------------------------
Belos: Operation Prec*x                              0.007409 (275)
Belos: Orthogonalization                             0.01177 (275)
Epetra_CrsMatrix::Multiply(TransA,X,Y)               0.005537 (280)
Epetra_CrsMatrix::Solve(Upper,Trans,UnitDiag,X,Y)    0.006862 (550)
Ifpack_ILU::ApplyInverse                             0.007275 (275)
Ifpack_ILU::ApplyInverse - Solve                     0.007074 (275)
Ifpack_ILU::Compute                                  0.002538 (1)
Ifpack_ILU::ComputeSetup                             0.0008707 (1)
Ifpack_ILU::Initialize                               0.0004559 (1)
================================================================================
Anasazi::BlockKrylovSchurSolMgr::solve() caught unexpected exception from Anasazi::BlockKrylovSchur::iterate() at iteration 1

Throw number = 1

Throw test that evaluated to true: ret != 0

Anasazi::OperatorTraits<double,Epetra_Multivector,Epetra_Operator>::Apply(): Error in Epetra_Operator::Apply(). Code -1
Anasazi::BlockKrylovSchurSolMgr::solve() returning Unconverged with no solutions.

--

Andris Freimanis

PhD student

Riga Technical university

Institute of transporation

engineering

Ķīpsalas iela 6a, Riga, Latvia, LV1048

www.rtu.lv<http://www.rtu.lv>
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