NAG CL Interface
f12asc (complex_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 f12arc need not be called.
If, however, you wish to reset some or all of the settings please refer to Section 11 in f12arc for a detailed description of the specification of the optional parameters.
1
Purpose
f12asc can be used to return additional monitoring information during computation. It is in a suite of functions consisting of
f12anc,
f12apc,
f12aqc,
f12arc and
f12asc.
2
Specification
The function may be called by the names: f12asc, nag_sparseig_complex_monit or nag_complex_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 complex eigenvalue problem , or of a generalized complex eigenvalue problem of order , where is large and the coefficient matrices and are sparse and complex. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense complex problems.
On an intermediate exit from
f12apc with
,
f12asc may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by
f12asc is:
-
–the number of the current Arnoldi iteration;
-
–the number of converged eigenvalues at this point;
-
–the converged eigenvalues;
-
–the error bounds on the converged eigenvalues.
f12asc 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).
f12asc should not be called at any time other than immediately following an
return from
f12apc.
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:
– Complex
Output
-
Note: the dimension,
dim, of the array
ritz
must be at least
(see
f12anc).
On exit: the first
nconv locations of the array
ritz contain the converged approximate eigenvalues.
-
4:
– Complex
Output
-
Note: the dimension,
dim, of the array
rzest
must be at least
(see
f12anc).
On exit: the first
nconv locations of the array
rzest contain the complex Ritz estimates on the 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
f12anc).
On entry: the array
icomm output by the preceding call to
f12apc.
-
6:
– const Complex
Communication Array
-
Note: the dimension,
dim, of the array
comm
must be at least
, where
lcomm
is passed to the setup function
(see
f12anc).
On entry: the array
comm output by the preceding call to
f12apc.
6
Error Indicators and Warnings
None.
7
Accuracy
A Ritz value,
, is deemed to have converged if the magnitude of 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.
f12asc is not threaded in any implementation.
None.
10
Example
This example solves in shifted-inverse mode, where and are obtained from the standard central difference discretization of the one-dimensional convection-diffusion operator on , with zero Dirichlet boundary conditions. The shift, , is a complex number, and the operator used in the shifted-inverse iterative process is .
10.1
Program Text
10.2
Program Data
10.3
Program Results