naginterfaces.library.sparseig.real_​symm_​monit

naginterfaces.library.sparseig.real_symm_monit(comm)

real_symm_monit can be used to return additional monitoring information during computation. It is in a suite of functions which includes real_symm_init(), real_symm_iter(), real_symm_proc() and real_symm_option().

For full information please refer to the NAG Library document for f12fe

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f12/f12fef.html

Parameters

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to real_symm_init().

Returns

niterint

The number of the current Arnoldi iteration.

nconvint

The number of converged eigenvalues so far.

ritzfloat, ndarray, shape $\left(\text{ncv}\right)$

The first $nconv$ locations of the array $ritz$ contain the real converged approximate eigenvalues.

rzestfloat, ndarray, shape $\left(\text{ncv}\right)$

The first $nconv$ locations of the array $rzest$ contain the Ritz estimates (error bounds) on the real $nconv$ converged approximate eigenvalues.

Notes

The suite of functions is designed to calculate some of the eigenvalues, $\lambda$, (and optionally the corresponding eigenvectors, $x$) of a standard eigenvalue problem $Ax=\lambda x$, or of a generalized eigenvalue problem $Ax=\lambda Bx$ of order $n$, where $n$ is large and the coefficient matrices $A$ and $B$ are sparse, real and symmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and symmetric problems.

On an intermediate exit from real_symm_iter() with $\text{irevcm}=4$, real_symm_monit may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by real_symm_monit is:

• the number of the current Arnoldi iteration;

• the number of converged eigenvalues at this point;

• the real and imaginary parts of the converged eigenvalues;

• the error bounds on the converged eigenvalues.

real_symm_monit does not have an equivalent function from the ARPACK package which prints various levels of detail of monitoring information through an output channel controlled via an argument value (see Lehoucq et al. (1998) for details of ARPACK routines). real_symm_monit should not be called at any time other than immediately following an $\text{irevcm}=4$ return from real_symm_iter().

References

Lehoucq, R B, 2001, Implicitly restarted Arnoldi methods and subspace iteration, SIAM Journal on Matrix Analysis and Applications (23), 551–562

Lehoucq, R B and Scott, J A, 1996, An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices, Preprint MCS-P547-1195, Argonne National Laboratory

Lehoucq, R B and Sorensen, D C, 1996, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM Journal on Matrix Analysis and Applications (17), 789–821

Lehoucq, R B, Sorensen, D C and Yang, C, 1998, ARPACK Users’ Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia