NAG FL Interface
f12aff (real_​band_​init)

1 Purpose

2 Specification

3 Description

4 References

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 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: $\mathbf{icomm}\left(\max \left(1,\mathbf{licomm}\right)\right)$ – Integer array Communication Array

On exit: contains data to be communicated to f12agf.

5: $\mathbf{licomm}$ – Integer Input

On entry: the dimension of the array icomm as declared in the (sub)program from which f12aff 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: $\mathbf{licomm}\ge 140\text{ or }\mathbf{licomm}=-1$.

6: $\mathbf{comm}\left(\max \left(1,\mathbf{lcomm}\right)\right)$ – Real (Kind=nag_wp) array Communication Array

On exit: contains data to be communicated to f12agf.

7: $\mathbf{lcomm}$ – Integer Input

On entry: the dimension of the array comm as declared in the (sub)program from which f12aff is called.

If $\mathbf{lcomm}=-1$, a workspace query is assumed and the routine only calculates the dimensions of icomm and comm required by f12agf, which it returns in $\mathbf{icomm}\left(1\right)$ and $\mathbf{comm}\left(1\right)$ respectively.

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

8: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ 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

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}>0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{nev}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nev}>0$.

$\mathbf{ifail}=3$

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 $\mathbf{ncv}\le \mathbf{n}$.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=5$

The length of the integer array comm is too small $\mathbf{lcomm}=〈\mathit{\text{value}}〉$, but must be at least $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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

8 Parallelism and Performance

9 Further Comments

10 Example