NAG FL Interface
f12fcf (real_symm_proc)
Note: this routine 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 routine f12fdf need not be called.
If, however, you wish to reset some or all of the settings please refer to Section 11 in f12fdf for a detailed description of the specification of the optional parameters.
1
Purpose
f12fcf is a post-processing routine in a suite of routines which includes
f12faf,
f12fbf,
f12fdf and
f12fef.
f12fcf must be called following a final exit from
f12fbf.
2
Specification
Fortran Interface
Subroutine f12fcf ( |
nconv, d, z, ldz, sigma, resid, v, ldv, comm, icomm, ifail) |
Integer, Intent (In) |
:: |
ldz, ldv |
Integer, Intent (Inout) |
:: |
icomm(*), ifail |
Integer, Intent (Out) |
:: |
nconv |
Real (Kind=nag_wp), Intent (In) |
:: |
sigma, resid(*) |
Real (Kind=nag_wp), Intent (Inout) |
:: |
d(*), z(ldz,*), v(ldv,*), comm(*) |
|
C Header Interface
#include <nag.h>
void |
f12fcf_ (Integer *nconv, double d[], double z[], const Integer *ldz, const double *sigma, const double resid[], double v[], const Integer *ldv, double comm[], Integer icomm[], Integer *ifail) |
|
C++ Header Interface
#include <nag.h> extern "C" {
void |
f12fcf_ (Integer &nconv, double d[], double z[], const Integer &ldz, const double &sigma, const double resid[], double v[], const Integer &ldv, double comm[], Integer icomm[], Integer &ifail) |
}
|
The routine may be called by the names f12fcf or nagf_sparseig_real_symm_proc.
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.
Following a call to
f12fbf,
f12fcf returns the converged approximations to eigenvalues and (optionally) the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace. The eigenvalues (and eigenvectors) are selected from those of a standard or generalized eigenvalue problem defined by real symmetric matrices. There is negligible additional cost to obtain eigenvectors; an orthonormal basis is always computed, but there is an additional storage cost if both are requested.
f12fcf is based on the routine
dseupd from the ARPACK package, which uses the Implicitly Restarted Lanczos iteration method. The method is described in
Lehoucq and Sorensen (1996) and
Lehoucq (2001) while its use within the ARPACK software is described in great detail in
Lehoucq et al. (1998). An evaluation of software for computing eigenvalues of sparse symmetric matrices is provided in
Lehoucq and Scott (1996). This suite of routines offers the same functionality as the ARPACK software for real symmetric problems, but the interface design is quite different in order to make the option setting clearer and to simplify some of the interfaces.
f12fcf, is a post-processing routine that must be called following a successful final exit from
f12fbf.
f12fcf uses data returned from
f12fbf and options, set either by default or explicitly by calling
f12fdf, to return the converged approximations to selected eigenvalues and (optionally):
-
–the corresponding approximate eigenvectors;
-
–an orthonormal basis for the associated approximate invariant subspace;
-
–both.
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
Output
-
On exit: the number of converged eigenvalues as found by
f12fbf.
-
2:
– Real (Kind=nag_wp) array
Output
-
Note: the dimension of the array
d
must be at least
(see
f12faf).
On exit: the first
nconv locations of the array
d contain the converged approximate eigenvalues.
-
3:
– Real (Kind=nag_wp) array
Output
-
Note: the second dimension of the array
z
must be at least
if the default option
has been selected and at least
if the option
or
has been selected (see
f12faf).
On exit: if the default option
(see
f12fdf) has been selected then
z contains the final set of eigenvectors corresponding to the eigenvalues held in
d. The real eigenvector associated with an eigenvalue is stored in the corresponding column of
z.
-
4:
– Integer
Input
-
On entry: the first dimension of the array
z as declared in the (sub)program from which
f12fcf is called.
Constraints:
- if the default option has been selected, ;
- if the option has been selected, .
-
5:
– Real (Kind=nag_wp)
Input
-
On entry: if one of the
Shifted Inverse (see
f12fdf) modes has been selected then
sigma contains the real shift used; otherwise
sigma is not referenced.
-
6:
– Real (Kind=nag_wp) array
Input
-
Note: the dimension of the array
resid
must be at least
(see
f12faf).
On entry: must not be modified following a call to
f12fbf since it contains data required by
f12fcf.
-
7:
– Real (Kind=nag_wp) array
Input/Output
-
Note: the second dimension of the array
v
must be at least
(see
f12faf).
On entry: the
ncv columns of
v contain the Lanczos basis vectors for
as constructed by
f12fbf.
On exit: if the option
has been set, or the option
has been set and a separate array
z has been passed (i.e.,
z does not equal
v), then the first
nconv columns of
v will contain approximate Schur vectors that span the desired invariant subspace.
-
8:
– Integer
Input
-
On entry: the first dimension of the array
v as declared in the (sub)program from which
f12fcf is called.
Constraint:
.
-
9:
– Real (Kind=nag_wp) array
Communication Array
-
Note: the actual argument supplied
must be the array
comm supplied to the initialization routine
f12faf.
On initial entry: must remain unchanged from the prior call to
f12faf.
On exit: contains data on the current state of the solution.
-
10:
– Integer array
Communication Array
-
Note: the actual argument supplied
must be the array
icomm supplied to the initialization routine
f12faf.
On initial entry: must remain unchanged from the prior call to
f12faf.
On exit: contains data on the current state of the solution.
-
11:
– 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,
,
in
f12faf.
Constraint:
(see
n in
f12faf).
-
On entry, , but this is not yet implemented.
-
The number of eigenvalues found to sufficient accuracy, as communicated through the argument
icomm, is zero. You should experiment with different values of
nev and
ncv, or select a different computational mode or increase the maximum number of iterations prior to calling
f12fbf.
-
Got a different count of the number of converged Ritz values than the value passed to it through the argument
icomm: number counted
, number expected
. This usually indicates that a communication array has been altered or has become corrupted between calls to
f12fbf and
f12fcf.
-
During calculation of a tridiagonal form, there was a failure to compute eigenvalues in a total of iterations.
-
Either the routine was called out of sequence (following an initial call to the setup routine and following completion of calls to the reverse communication routine) or the communication arrays have become corrupted.
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
The relative accuracy of a Ritz value,
, is considered acceptable if its Ritz estimate
. The default
Tolerance used is the
machine precision given by
x02ajf.
8
Parallelism and Performance
f12fcf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f12fcf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
None.
10
Example
This example solves in regular mode, where and are obtained from the standard central difference discretization of the one-dimensional Laplacian operator
on , with zero Dirichlet boundary conditions.
10.1
Program Text
10.2
Program Data
10.3
Program Results