NAG Library Function Document

nag_complex_banded_eigensystem_init (f12atc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{n}$ – IntegerInput

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:    $\mathbf{nev}$ – IntegerInput

On entry: the number of eigenvalues to be computed.

Constraint: $0<\mathbf{nev}<\mathbf{n}-1$.

3:    $\mathbf{ncv}$ – IntegerInput

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 $\mathbf{ncv}\ge 2\times \mathbf{nev}+1$. 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 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:    $\mathbf{icomm}\left[\max \left(1,\mathbf{licomm}\right)\right]$ – IntegerCommunication Array

On exit: contains data to be communicated to nag_complex_banded_eigensystem_solve (f12auc).

5:    $\mathbf{licomm}$ – IntegerInput

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: $\mathbf{licomm}\ge 140\text{ or }\mathbf{licomm}=-1$.

6:    $\mathbf{comm}\left[\max \left(1,\mathbf{lcomm}\right)\right]$ – ComplexCommunication Array

On exit: contains data to be communicated to nag_complex_banded_eigensystem_solve (f12auc).

7:    $\mathbf{lcomm}$ – IntegerInput

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 nag_complex_banded_eigensystem_solve (f12auc), which it returns in $\mathbf{icomm}\left[0\right]$ and $\mathbf{comm}\left[0\right]$ respectively.

Constraint: $\mathbf{lcomm}\ge 60\text{ or }\mathbf{lcomm}=-1$.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.

NE_BAD_PARAM

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example