NAG Library Function Document
nag_complex_sparse_eigensystem_init (f12anc)
1
Purpose
nag_complex_sparse_eigensystem_init (f12anc) is a setup function in a suite of functions consisting of
nag_complex_sparse_eigensystem_init (f12anc),
nag_complex_sparse_eigensystem_iter (f12apc),
nag_complex_sparse_eigensystem_sol (f12aqc),
nag_complex_sparse_eigensystem_option (f12arc) and
nag_complex_sparse_eigensystem_monit (f12asc). It is used to find some of the eigenvalues (and optionally the corresponding eigenvectors) of a standard or generalized eigenvalue problem defined by complex nonsymmetric matrices.
The suite of functions is suitable for the solution of large sparse, standard or generalized, nonsymmetric complex eigenproblems where only a few eigenvalues from a selected range of the spectrum are required.
2
Specification
#include <nag.h> |
#include <nagf12.h> |
void |
nag_complex_sparse_eigensystem_init (Integer n,
Integer nev,
Integer ncv,
Integer icomm[],
Integer licomm,
Complex comm[],
Integer lcomm,
NagError *fail) |
|
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, complex and nonsymmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, complex and nonsymmetric problems.
nag_complex_sparse_eigensystem_init (f12anc) is a setup function which must be called before
nag_complex_sparse_eigensystem_iter (f12apc), the reverse communication iterative solver, and before
nag_complex_sparse_eigensystem_option (f12arc), the options setting function.
nag_complex_sparse_eigensystem_sol (f12aqc) is a post-processing function that must be called following a successful final exit from
nag_complex_sparse_eigensystem_iter (f12apc), while
nag_complex_sparse_eigensystem_monit (f12asc) can be used to return additional monitoring information during the computation.
This setup function initializes the communication arrays, sets (to their default values) all options that can be set by you via the option setting function
nag_complex_sparse_eigensystem_option (f12arc), 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
nag_complex_sparse_eigensystem_option (f12arc).
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:
– IntegerInput
-
On entry: the order of the matrix (and the order of the matrix for the generalized problem) that defines the eigenvalue problem.
Constraint:
.
- 2:
– IntegerInput
-
On entry: the number of eigenvalues to be computed.
Constraint:
.
- 3:
– IntegerInput
-
On entry: the number of Arnoldi 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:
– IntegerCommunication Array
-
On exit: contains data to be communicated to the other functions in the suite.
- 5:
– IntegerInput
-
On entry: the dimension of the array
icomm.
If
, a workspace query is assumed and the function only calculates the required dimensions of
icomm and
comm, which it returns in
and
respectively.
Constraint:
.
- 6:
– ComplexCommunication Array
-
On exit: contains data to be communicated to the other functions in the suite.
- 7:
– IntegerInput
-
On entry: the dimension of the array
comm.
If
, a workspace query is assumed and the function only calculates the dimensions of
icomm and
comm required by
nag_complex_sparse_eigensystem_iter (f12apc), which it returns in
and
respectively.
Constraint:
.
- 8:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INT_2
-
The length of the integer array
icomm is too small
, but must be at least
.
- NE_INT_3
-
On entry, , and .
Constraint: .
On entry, , and .
Constraint: and .
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
7
Accuracy
Not applicable.
8
Parallelism and Performance
nag_complex_sparse_eigensystem_init (f12anc) 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 convection-diffusion operator on the unit square, with zero Dirichlet boundary conditions. The eigenvalues of largest magnitude are found.
10.1
Program Text
Program Text (f12ance.c)
10.2
Program Data
Program Data (f12ance.d)
10.3
Program Results
Program Results (f12ance.r)