[Trilinos-Users] Anasazi/LOBPCG question

[David Hysom]

Hi,

In our codes we're using LOBPCG to solve for either the largest two
or smallest two eigenvalues. Our graphs are scale-free (e.g, orkut
and amazon, from the SNAP collection). When solving for the largest
two eigenpairs LOBPCG reports convergence, but the residuals
sometimes do not meet our convergence criteria; this doesn't happen
when solving for the two smallest eigenvalues. Could you comment
on this? Thanks, David

Example, convergence tolerance asked for: 1e-5

The number of iterations performed is 9
The current block size is             2
The number of auxiliary vectors is    0
The number of operations Op*x   is 20
The number of operations M*x    is 0
The number of operations Prec*x is 0

CURRENT EIGENVALUE ESTIMATES
           Eigenvalue         Residual(M)         Residual(2)
--------------------------------------------------------------------------------
         1.481700e+04         not current 1.154163e-02
         1.287200e+04         not current 7.935646e-02
================================================================================

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

                                       TimeMonitor results over 64 
processors

Timer Name                              MinOverProcs MeanOverProcs     
MaxOverProcs     MeanOverCallCounts
------------------------------------------------------------------------------------------------------------------
Anasazi: LOBPCG::Computing residuals    0.006275 (10)    0.006756 
(10)     0.007093 (10)    0.0006756 (10)
Anasazi: LOBPCG::Direct solve           0.00112 (10)     0.001218 
(10)     0.001451 (10)    0.0001218 (10)
Anasazi: LOBPCG::Initialization         0.3974 (2)       0.3978 
(2)        0.3984 (2)       0.1989 (2)
Anasazi: LOBPCG::Local projection       0.02566 (10)     0.5958 
(10)       0.7844 (10)      0.05958 (10)
Anasazi: LOBPCG::Local update           0.05916 (10)     0.06023 
(10)      0.06112 (10)     0.006023 (10)
Anasazi: LOBPCG::Operation M*x          0 (0)            0 
(0)             0 (0)            0 (0)
Anasazi: LOBPCG::Operation Op*x         0.349 (10)       0.5372 
(10)       1.107 (10)       0.05372 (10)
Anasazi: LOBPCG::Operation Prec*x       0 (0)            0 
(0)             0 (0)            0 (0)
Anasazi: LOBPCG::Orthogonalization      0.2928 (10)      0.2937 
(10)       0.2949 (10)      0.02937 (10)
Anasazi: LOBPCG::Sorting eigenvalues    4.1e-05 (10)     5.239e-05 
(10)    0.000107 (10)    5.239e-06 (10)
------------------------------------------------------------------------------------------------------------------
Anasazi: LOBPCGSolMgr locking           0 (0)            0 
(0)             0 (0)            0 (0)
Anasazi: LOBPCGSolMgr::solve()          1.501 (1)        1.502 
(1)         1.502 (1)        1.502 (1)
==================================================================================================================
LOBPCG converged in 9 iterations