[Trilinos-Users] Anasazi/LOBPCG question

[Alicia Klinvex]

Hello David,

By default, Anasazi eigensolvers scale the residuals by the eigenvalue.
The RELATIVE residual norm(r)/lambda is less than 1e-5 in your case,
although the absolute residual is much larger.  To turn this off, you want
to set the parameter "Relative Convergence Tolerance" to false.

Best wishes,
Alicia Klinvex

On Tue, Mar 31, 2015 at 12:14 PM, David Hysom <hysom1 at llnl.gov> wrote:

> 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
>
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