NAG CL Interfacef12atc (complex_​band_​init)

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1Purpose

f12atc is a setup function for f12auc which may be used for finding some eigenvalues (and optionally the corresponding eigenvectors) of a standard or generalized eigenvalue problem defined by complex, banded, non-Hermitian matrices. The banded matrix must be stored using the LAPACK column ordered storage format for complex banded non-Hermitian matrices (see Section 3.4.4 in the F07 Chapter Introduction).

2Specification

 #include
 void f12atc (Integer n, Integer nev, Integer ncv, Integer icomm[], Integer licomm, Complex comm[], Integer lcomm, NagError *fail)
The function may be called by the names: f12atc, nag_sparseig_complex_band_init or nag_complex_banded_eigensystem_init.

3Description

The pair of functions f12atc and f12auc together with the option setting function f12arc are designed to calculate some of the eigenvalues, $\lambda$, (and optionally the corresponding eigenvectors, $x$) of a standard eigenvalue problem $Ax=\lambda x$, or of a generalized eigenvalue problem $Ax=\lambda Bx$ of order $n$, where $n$ is large and the coefficient matrices $A$ and $B$ are banded complex and non-Hermitian.
f12atc is a setup function which must be called before the option setting function f12arc and the solver function f12auc. Internally, f12auc makes calls to f12apc and f12aqc; the function documents for f12apc and f12aqc should be consulted for details of the algorithm used.
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 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 f12arc.

4References

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

5Arguments

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 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 ${\mathbf{ncv}}\ge 2×{\mathbf{nev}}+1$. 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 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: ${\mathbf{nev}}+1<{\mathbf{ncv}}\le {\mathbf{n}}$.
4: $\mathbf{icomm}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{licomm}}\right)\right]$Integer Communication Array
On exit: contains data to be communicated to f12auc.
5: $\mathbf{licomm}$Integer Input
On entry: the dimension of the array icomm.
If ${\mathbf{licomm}}=-1$, a workspace query is assumed and the function only calculates the required dimensions of icomm and comm, which it returns in ${\mathbf{icomm}}\left[0\right]$ and ${\mathbf{comm}}\left[0\right]$ 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 Communication Array
On exit: contains data to be communicated to f12auc.
7: $\mathbf{lcomm}$Integer Input
On entry: the dimension of the array comm.
If ${\mathbf{lcomm}}=-1$, a workspace query is assumed and the function only calculates the dimensions of icomm and comm required by f12auc, which it returns in ${\mathbf{icomm}}\left[0\right]$ and ${\mathbf{comm}}\left[0\right]$ respectively.
Constraint: ${\mathbf{lcomm}}\ge 60$ or ${\mathbf{lcomm}}=-1$.
8: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error 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.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}>0$.
On entry, ${\mathbf{nev}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{nev}}>0$.
The length of the complex array comm is too small ${\mathbf{lcomm}}=⟨\mathit{\text{value}}⟩$, but must be at least $⟨\mathit{\text{value}}⟩$.
The length of the integer array icomm is too small ${\mathbf{licomm}}=⟨\mathit{\text{value}}⟩$, but must be at least $⟨\mathit{\text{value}}⟩$.
NE_INT_3
On entry, ${\mathbf{ncv}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{nev}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ncv}}>{\mathbf{nev}}+1$ and ${\mathbf{ncv}}\le {\mathbf{n}}$.
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.

Not applicable.