f12fff is a setup routine for f12fgf which can be used to find some eigenvalues (and optionally the corresponding eigenvectors) of a standard or generalized eigenvalue problem defined by real, banded, symmetric matrices. The banded matrix must be stored using the LAPACK storage format for real banded nonsymmetric matrices.

2 Specification

Fortran Interface

Subroutine f12fff (

n, nev, ncv, icomm, licomm, comm, lcomm, ifail)

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	f12fff_ (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 f12fff or nagf_sparseig_real_symm_band_init.

3 Description

The pair of routines f12fff and f12fgf together with the option setting routine f12fdf are designed to calculate some of the eigenvalues,

λ

, (and optionally the corresponding eigenvectors,

x

) of a standard eigenvalue problem

A x = λ x

, or of a generalized eigenvalue problem

A x = λ B x

of order

n

, where

n

is large and the coefficient matrices

A

and

B

are banded real and symmetric.

f12fff is a setup routine which must be called before the option setting routine f12fdf and the solver routine f12fgf. Internally, f12fgf makes calls to f12fbf and f12fcf; the routine documents for f12fbf and f12fcf should be consulted for details of the algorithm used.

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, Philadelphia

5 Arguments

1: $n$ – Integer Input: On entry: the order of the matrix $A$ (and the order of the matrix $B$ for the generalized problem) that defines the eigenvalue problem.

Constraint: $n > 0$ .
2: $nev$ – Integer Input: On entry: the number of eigenvalues to be computed.

Constraint: $0 < nev < n - 1$ .
3: $ncv$ – 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 $ncv \geq 2 \times nev + 1$ . 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: $nev < ncv \leq n$ .
4: $icomm (\max (1, licomm))$ – Integer array Communication Array: On exit: contains data to be communicated to f12fgf.
5: $licomm$ – Integer Input: On entry: the dimension of the array icomm as declared in the (sub)program from which f12fff is called.
If $licomm = - 1$ , a workspace query is assumed and the routine only calculates the required dimensions of icomm and comm, which it returns in $icomm (1)$ and $comm (1)$ respectively.

Constraint: $licomm \geq 140$ or $licomm = - 1$ .
6: $comm (\max (1, lcomm))$ – Real (Kind=nag_wp) array Communication Array: On exit: contains data to be communicated to f12fgf.
7: $lcomm$ – Integer Input: On entry: the dimension of the array comm as declared in the (sub)program from which f12fff is called.
If $lcomm = - 1$ , a workspace query is assumed and the routine only calculates the dimensions of icomm and comm required by f12fgf, which it returns in $icomm (1)$ and $comm (1)$ respectively.

Constraint: $lcomm \geq 60$ or $lcomm = - 1$ .
8: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $- 1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $- 1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $- 1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n > 0$ .

$ifail = 2$: On entry, $nev = ⟨ value ⟩$ .
Constraint: $nev > 0$ .

$ifail = 3$: On entry, $ncv = ⟨ value ⟩$ , $nev = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $ncv > nev + 1$ and $ncv \leq n$ .

$ifail = 4$: The length of the integer array icomm is too small $licomm = ⟨ value ⟩$ , but must be at least $⟨ value ⟩$ .

$ifail = 5$: The length of the integer array comm is too small $lcomm = ⟨ value ⟩$ , but must be at least $⟨ value ⟩$ .

$ifail = - 99$: 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.

$ifail = - 399$: 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.