NAG CL Interface
f12aec (real_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 f12adc need not be called.
If, however, you wish to reset some or all of the settings please refer to Section 11 in f12adc for a detailed description of the specification of the optional parameters.
1
Purpose
f12aec can be used to return additional monitoring information during computation. It is in a suite of functions consisting of
f12aac,
f12abc,
f12acc,
f12adc and
f12aec.
2
Specification
The function may be called by the names: f12aec, nag_sparseig_real_monit or nag_real_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 nonsymmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and nonsymmetric problems.
On an intermediate exit from
f12abc with
,
f12aec may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by
f12aec 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.
f12aec 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).
f12aec should not be called at any time other than immediately following an
return from
f12abc.
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
ritzr
must be at least
(see
f12aac).
On exit: the first
nconv locations of the array
ritzr contain the real parts of the converged approximate eigenvalues.
-
4:
– double
Output
-
Note: the dimension,
dim, of the array
ritzi
must be at least
(see
f12aac).
On exit: the first
nconv locations of the array
ritzi contain the imaginary parts of the converged approximate eigenvalues.
-
5:
– double
Output
-
Note: the dimension,
dim, of the array
rzest
must be at least
(see
f12aac).
On exit: the first
nconv locations of the array
rzest contain the Ritz estimates (error bounds) on the converged approximate eigenvalues.
-
6:
– 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
f12aac).
On entry: the array
icomm output by the preceding call to
f12abc.
-
7:
– 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
f12aac).
On entry: the array
comm output by the preceding call to
f12abc.
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
f12aec is not threaded in any implementation.
None.
10
Example
This example solves in shifted-real mode, where is the tridiagonal matrix with on the diagonal, on the subdiagonal and on the superdiagonal. The matrix is the tridiagonal matrix with on the diagonal and on the off-diagonals. The shift sigma, , is a complex number, and the operator used in the shifted-real iterative process is .
10.1
Program Text
10.2
Program Data
10.3
Program Results