NAG CL Interface
f12fec (real_symm_monit)
Note: this function uses optional parameters to define choices in the problem specification. If you wish to use default
settings for all of the optional parameters, then the option setting function f12fdc need not be called.
If, however, you wish to reset some or all of the settings please refer to Section 11 in f12fdc for a detailed description of the specification of the optional parameters.
1
Purpose
f12fec can be used to return additional monitoring information during computation. It is in a suite of functions which includes
f12fac,
f12fbc,
f12fcc and
f12fdc.
2
Specification
The function may be called by the names: f12fec, nag_sparseig_real_symm_monit or nag_real_symm_sparse_eigensystem_monit.
3
Description
The suite of functions is designed to calculate some of the eigenvalues, , (and optionally the corresponding eigenvectors, ) of a standard eigenvalue problem , or of a generalized eigenvalue problem of order , where is large and the coefficient matrices and 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
f12fbc with
,
f12fec may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by
f12fec 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.
f12fec 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).
f12fec should not be called at any time other than immediately following an
return from
f12fbc.
4
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
5
Arguments
-
1:
– Integer *
Output
-
On exit: the number of the current Arnoldi iteration.
-
2:
– Integer *
Output
-
On exit: the number of converged eigenvalues so far.
-
3:
– double
Output
-
Note: the dimension,
dim, of the array
ritz
must be at least
(see
f12fac).
On exit: the first
nconv locations of the array
ritz contain the real converged approximate eigenvalues.
-
4:
– double
Output
-
Note: the dimension,
dim, of the array
rzest
must be at least
(see
f12fac).
On exit: the first
nconv locations of the array
rzest contain the Ritz estimates (error bounds) on the real
nconv converged approximate eigenvalues.
-
5:
– const Integer
Communication Array
-
Note: the dimension,
dim, of the array
icomm
must be at least
, where
licomm
is passed to the setup function
(see
f12fac).
On entry: the array
icomm output by the preceding call to
f12fbc.
-
6:
– const double
Communication Array
-
Note: the dimension,
dim, of the array
comm
must be at least
, where
lcomm
is passed to the setup function
(see
f12fac).
On entry: the array
comm output by the preceding call to
f12fbc.
6
Error Indicators and Warnings
None.
7
Accuracy
A Ritz value,
, is deemed to have converged if its Ritz estimate
. The default
used is the
machine precision given by
X02AJC.
8
Parallelism and Performance
Background information to multithreading can be found in the
Multithreading documentation.
f12fec is not threaded in any implementation.
None.
10
Example
This example solves
using the
option (see
f12fdc, where
and
are obtained by the finite element method applied to the one-dimensional discrete Laplacian operator
on
, with zero Dirichlet boundary conditions using piecewise linear elements. The shift,
, is a real number, and the operator used in the Buckling iterative process is
and
.
10.1
Program Text
10.2
Program Data
10.3
Program Results