NAG FL Interface
f12faf (real_symm_init)
1
Purpose
f12faf is a setup routine in a suite of routines consisting of
f12faf,
f12fbf,
f12fcf,
f12fdf and
f12fef. It is used to find some of the eigenvalues (and optionally the corresponding eigenvectors) of a standard or generalized eigenvalue problem defined by real symmetric matrices.
The suite of routines is suitable for the solution of large sparse, standard or generalized, symmetric eigenproblems where only a few eigenvalues from a selected range of the spectrum are required.
2
Specification
Fortran Interface
Integer, Intent (In) |
:: |
n, nev, ncv, licomm, lcomm |
Integer, Intent (Inout) |
:: |
ifail |
Integer, Intent (Out) |
:: |
icomm(max(1,licomm)) |
Real (Kind=nag_wp), Intent (Out) |
:: |
comm(max(1,lcomm)) |
|
C Header Interface
#include <nag.h>
void |
f12faf_ (const Integer *n, const Integer *nev, const Integer *ncv, Integer icomm[], const Integer *licomm, double comm[], const Integer *lcomm, Integer *ifail) |
|
C++ Header Interface
#include <nag.h> extern "C" {
void |
f12faf_ (const Integer &n, const Integer &nev, const Integer &ncv, Integer icomm[], const Integer &licomm, double comm[], const Integer &lcomm, Integer &ifail) |
}
|
The routine may be called by the names f12faf or nagf_sparseig_real_symm_init.
3
Description
The suite of routines 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.
f12faf is a setup routine which must be called before
f12fbf, the reverse communication iterative solver, and before
f12fdf, the options setting routine.
f12fcf, is a post-processing routine that must be called following a successful final exit from
f12fbf, while
f12fef can be used to return additional monitoring information during the computation.
This setup routine initializes the communication arrays, sets (to their default values) all options that can be set by you via the option setting routine
f12fdf, and checks that the lengths of the communication arrays as passed by you are of sufficient length. For details of the options available and how to set them see
Section 11.1 in
f12fdf.
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, Philidelphia
5
Arguments
-
1:
– Integer
Input
-
On entry: the order of the matrix (and the order of the matrix for the generalized problem) that defines the eigenvalue problem.
Constraint:
.
-
2:
– Integer
Input
-
On entry: the number of eigenvalues to be computed.
Constraint:
.
-
3:
– Integer
Input
-
On entry: the number of Lanczos basis vectors to use during the computation.
At present there is no
a priori analysis to guide the selection of
ncv relative to
nev. However, it is recommended that
. If many problems of the same type are to be solved, you should experiment with increasing
ncv while keeping
nev fixed for a given test problem. This will usually decrease the required number of matrix-vector operations but it also increases the work and storage required to maintain the orthogonal basis vectors. The optimal ‘cross-over’ with respect to CPU time is problem dependent and must be determined empirically.
Constraint:
.
-
4:
– Integer array
Communication Array
-
On exit: contains data to be communicated to the other routines in the suite.
-
5:
– Integer
Input
-
On entry: the dimension of the array
icomm as declared in the (sub)program from which
f12faf is called.
If
, a workspace query is assumed and the routine only calculates the required dimensions of
icomm and
comm, which it returns in
and
respectively.
Constraint:
.
-
6:
– Real (Kind=nag_wp) array
Communication Array
-
On exit: contains data to be communicated to the other routines in the suite.
-
7:
– Integer
Input
-
On entry: the dimension of the array
comm as declared in the (sub)program from which
f12faf is called.
If
, a workspace query is assumed and the routine only calculates the dimensions of
icomm and
comm required by
f12fbf, which it returns in
and
respectively.
Constraint:
.
-
8:
– Integer
Input/Output
-
On entry:
ifail must be set to
,
. If you are unfamiliar with this argument you should refer to
Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this argument, the recommended value is
.
When the value is used it is essential to test the value of ifail on exit.
On exit:
unless the routine detects an error or a warning has been flagged (see
Section 6).
6
Error Indicators and Warnings
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Errors or warnings detected by the routine:
-
On entry, .
Constraint: .
-
On entry, .
Constraint: .
-
On entry, , and .
Constraint: and .
-
The length of the integer array
icomm is too small
, but must be at least
.
-
On entry, , and .
Constraint: .
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See
Section 9 in the Introduction to the NAG Library FL Interface for further information.
7
Accuracy
Not applicable.
8
Parallelism and Performance
f12faf is not threaded in any implementation.
None.
10
Example
This example solves in regular mode, where is obtained from the standard central difference discretization of the Laplacian operator
on the unit square, with zero Dirichlet boundary conditions. Eigenvalues of smallest magnitude are selected.
10.1
Program Text
10.2
Program Data
10.3
Program Results