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

Thu Sep 14 10:31:35 EDT 2017

Hello Andris,

Your linear solver is converging; the eigensolver is not.  You said this problem was being solved correctly by scipi.  It’s possible that the eigensolver is failing to converge because your linear systems are not being solved accurately enough.  (Block Krylov Schur is sensitive to that.)  Do you know how scipi is solving the linear systems?

Best wishes,
Alicia

From: Andris Freimanis [mailto:andris.freimanis_1 at rtu.lv]
Sent: Thursday, September 14, 2017 9:20 AM
To: Klinvex, Alicia Marie <amklinv at sandia.gov>
Subject: Re: [EXTERNAL] [Trilinos-Users] Anasazi BlockKrylovSchur solver Error in F^H M F == I

Dear, Alicia,

I increased the number of blocks to 48 and to 239 (matrix size - 1), sadly solver still didn't converge. It's interesting that residual is less than the tolerance, but it shows no convergence.

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

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

*******************************************************
***** Belos Iterative Solver:  Block Gmres
***** Maximum Iterations: 1000
***** Block Size: 1
***** Residual Test:
*****   Test 1 : Belos::StatusTestImpResNorm<>: (2-Norm Res Vec) / (2-Norm Prec Res0), tol = 0.001
*******************************************************
Iter   82, [ 1] :    7.842584e-04
Belos::BlockGmresSolMgr::solve(): Warning! Solver has experienced a loss of accuracy!
Passed.......OR Combination ->
  OK...........Number of Iterations = 82 < 1000
  Converged....(2-Norm Res Vec) / (2-Norm Prec Res0)
               residual [ 0 ] = 7.842584e-04 < 1.000000e-03

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

On 2017.09.14. 16:09, Klinvex, Alicia Marie wrote:
Hello Andris,

Can you try increasing your number of blocks?  You allowed GMRES to store a subspace of size 24, and you allowed it 10 restarts, which is why it did not attempt 1000 iterations.

Best wishes,
Alicia

From: Andris Freimanis [mailto:andris.freimanis_1 at rtu.lv]
Sent: Thursday, September 14, 2017 9:03 AM
To: Klinvex, Alicia Marie <amklinv at sandia.gov><mailto:amklinv at sandia.gov>; Trilinos mailing list <trilinos-users at trilinos.org><mailto:trilinos-users at trilinos.org>
Subject: RE: [EXTERNAL] [Trilinos-Users] Anasazi BlockKrylovSchur solver Error in F^H M F == I

Dear, Alicia,

thank you for your response.

M is a part of a generalized eigenvalue problem A*x = lambda*M*x. Since A is real non-hermitian I'm using Block Krylov Schur eigensolver with shift-invert transformation as shown in BlockKrylovSchurEpetraExGenBelos.cpp example. And block GMRES linear solver with ILU preconditioner for the inverted part.
Linear solver parameters are:
    Block size 1
    Number of blocks 24
    Max iterations 1000 (if I understand the output correctly, only 264 were used)
    Max restarts 10
    Tolerance 1e-3
ILU preconditioner parameters were:
    Drop tolerance 1e-9
    Level-of-fill 1
    Schwartz: combine mode "Add"

Scipy's eigs function, which uses Arpack, solved this problem easily. So most likely I have made some mistake with Trilinos solvers.

Best regards,

Andris

On 2017.09.14. 15:06, Klinvex, Alicia Marie wrote:
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><mailto: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
/usr/local/trilinos/include/AnasaziEpetraAdapter.hpp:1401:

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>

--

Andris Freimanis

PhD student

Riga Technical university

Institute of transporation

engineering

Ķīpsalas iela 6a, Riga, Latvia, LV1048

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

--

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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