NAG CL Interface
f12fac (real_symm_init)
1
Purpose
f12fac is a setup function in a suite of functions consisting of
f12fac,
f12fbc,
f12fcc,
f12fdc and
f12fec. 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 functions 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
The function may be called by the names: f12fac, nag_sparseig_real_symm_init or nag_real_symm_sparse_eigensystem_init.
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 symmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and symmetric problems.
f12fac is a setup function which must be called before
f12fbc, the reverse communication iterative solver, and before
f12fdc, the options setting function.
f12fcc, is a post-processing function that must be called following a successful final exit from
f12fbc, while
f12fec 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
f12fdc, 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
f12fdc.
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
Communication Array
-
On exit: contains data to be communicated to the other functions in the suite.
-
5:
– Integer
Input
-
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:
– double
Communication Array
-
On exit: contains data to be communicated to the other functions in the suite.
-
7:
– Integer
Input
-
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
f12fbc, which it returns in
and
respectively.
Constraint:
.
-
8:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
7
Accuracy
Not applicable.
8
Parallelism and Performance
f12fac 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