NAG FL Interface
f12anf (complex_init)
1
Purpose
f12anf is a setup routine in a suite of routines consisting of
f12anf,
f12apf,
f12aqf,
f12arf and
f12asf. 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 routines 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
Fortran Interface
Integer, Intent (In) 
:: 
n, nev, ncv, licomm, lcomm 
Integer, Intent (Inout) 
:: 
ifail 
Integer, Intent (Out) 
:: 
icomm(max(1,licomm)) 
Complex (Kind=nag_wp), Intent (Out) 
:: 
comm(max(1,lcomm)) 

C Header Interface
#include <nag.h>
void 
f12anf_ (const Integer *n, const Integer *nev, const Integer *ncv, Integer icomm[], const Integer *licomm, Complex comm[], const Integer *lcomm, Integer *ifail) 

C++ Header Interface
#include <nag.h> extern "C" {
void 
f12anf_ (const Integer &n, const Integer &nev, const Integer &ncv, Integer icomm[], const Integer &licomm, Complex comm[], const Integer &lcomm, Integer &ifail) 
}

The routine may be called by the names f12anf or nagf_sparseig_complex_init.
3
Description
The suite of routines is designed to calculate some of the eigenvalues, $\lambda $, (and optionally the corresponding eigenvectors, $x$) of a standard complex eigenvalue problem $Ax=\lambda x$, or of a generalized complex eigenvalue problem $Ax=\lambda Bx$ of order $n$, where $n$ is large and the coefficient matrices $A$ and $B$ are sparse, complex and nonsymmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, complex and nonsymmetric problems.
f12anf is a setup routine which must be called before
f12apf, the reverse communication iterative solver, and before
f12arf, the options setting routine.
f12aqf is a postprocessing routine that must be called following a successful final exit from
f12apf, while
f12asf 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
f12arf, 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
f12arf.
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 MCSP5471195 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 Largescale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods SIAM, Philidelphia
5
Arguments

1:
$\mathbf{n}$ – 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:
${\mathbf{n}}>0$.

2:
$\mathbf{nev}$ – Integer
Input

On entry: the number of eigenvalues to be computed.
Constraint:
$0<{\mathbf{nev}}<{\mathbf{n}}1$.

3:
$\mathbf{ncv}$ – Integer
Input

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
${\mathbf{ncv}}\ge 2\times {\mathbf{nev}}+1$. 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 matrixvector operations but it also increases the work and storage required to maintain the orthogonal basis vectors. The optimal ‘crossover’ with respect to CPU time is problem dependent and must be determined empirically.
Constraint:
${\mathbf{nev}}+1<{\mathbf{ncv}}\le {\mathbf{n}}$.

4:
$\mathbf{icomm}\left(\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{licomm}}\right)\right)$ – Integer array
Communication Array

On exit: contains data to be communicated to the other routines in the suite.

5:
$\mathbf{licomm}$ – Integer
Input

On entry: the dimension of the array
icomm as declared in the (sub)program from which
f12anf is called.
If
${\mathbf{licomm}}=1$, a workspace query is assumed and the routine only calculates the required dimensions of
icomm and
comm, which it returns in
${\mathbf{icomm}}\left(1\right)$ and
${\mathbf{comm}}\left(1\right)$ respectively.
Constraint:
${\mathbf{licomm}}\ge 140$ or ${\mathbf{licomm}}=1$.

6:
$\mathbf{comm}\left(\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{lcomm}}\right)\right)$ – Complex (Kind=nag_wp) array
Communication Array

On exit: contains data to be communicated to the other routines in the suite.

7:
$\mathbf{lcomm}$ – Integer
Input

On entry: the dimension of the array
comm as declared in the (sub)program from which
f12anf is called.
If
${\mathbf{lcomm}}=1$, a workspace query is assumed and the routine only calculates the dimensions of
icomm and
comm required by
f12apf, which it returns in
${\mathbf{icomm}}\left(1\right)$ and
${\mathbf{comm}}\left(1\right)$ respectively.
Constraint:
${\mathbf{lcomm}}\ge 3\times {\mathbf{n}}+3\times {\mathbf{ncv}}\times {\mathbf{ncv}}+5\times {\mathbf{ncv}}+60$ or ${\mathbf{lcomm}}=1$.

8:
$\mathbf{ifail}$ – 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 $\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit:
${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see
Section 6).
6
Error Indicators and Warnings
If on entry
${\mathbf{ifail}}=0$ or
$1$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Errors or warnings detected by the routine:
 ${\mathbf{ifail}}=1$

On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}>0$.
 ${\mathbf{ifail}}=2$

On entry, ${\mathbf{nev}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{nev}}>0$.
 ${\mathbf{ifail}}=3$

On entry, ${\mathbf{ncv}}=\u2329\mathit{\text{value}}\u232a$, ${\mathbf{nev}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{ncv}}\ge {\mathbf{nev}}+1$ and ${\mathbf{ncv}}\le {\mathbf{n}}$.
 ${\mathbf{ifail}}=4$

The length of the integer array
icomm is too small
${\mathbf{licomm}}=\u2329\mathit{\text{value}}\u232a$, but must be at least
$\u2329\mathit{\text{value}}\u232a$.
 ${\mathbf{ifail}}=5$

On entry, ${\mathbf{lcomm}}=\u2329\mathit{\text{value}}\u232a$, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{ncv}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{lcomm}}\ge 3\times {\mathbf{n}}+3\times {\mathbf{ncv}}\times {\mathbf{ncv}}+5\times {\mathbf{ncv}}+60$.
 ${\mathbf{ifail}}=99$
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.
 ${\mathbf{ifail}}=399$
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.
 ${\mathbf{ifail}}=999$
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
f12anf is not threaded in any implementation.
None.
10
Example
This example solves $Ax=\lambda x$ in regular mode, where $A$ is obtained from the standard central difference discretization of the convectiondiffusion operator $\frac{{\partial}^{2}u}{\partial {x}^{2}}+\frac{{\partial}^{2}u}{\partial {y}^{2}}+\rho \frac{\partial u}{\partial x}$
on the unit square, with zero Dirichlet boundary conditions. The eigenvalues of largest magnitude are found.
10.1
Program Text
10.2
Program Data
10.3
Program Results