NAG Library Routine Document

F12ATF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     NEV – INTEGERInput

On entry: the number of eigenvalues to be computed.

Constraint: $0<\mathbf{NEV}<\mathbf{N}-1$.

3:     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:     ICOMM($\max \left(1,\mathbf{LICOMM}\right)$) – INTEGER arrayCommunication Array

On exit: contains data to be communicated to F12AUF.

5:     LICOMM – INTEGERInput

On entry: the dimension of the array ICOMM as declared in the (sub)program from which F12ATF 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:     COMM($\max \left(1,\mathbf{LCOMM}\right)$) – COMPLEX (KIND=nag_wp) arrayCommunication Array

On exit: contains data to be communicated to F12AUF.

7:     LCOMM – INTEGERInput

On entry: the dimension of the array COMM as declared in the (sub)program from which F12ATF is called.

If $\mathbf{LCOMM}=-1$, a workspace query is assumed and the routine only calculates the dimensions of ICOMM and COMM required by F12AUF, 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:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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 complex array COMM is too small $\mathbf{LCOMM}=⟨\mathit{\text{value}}⟩$, but must be at least $⟨\mathit{\text{value}}⟩$.

7  Accuracy

8  Further Comments

9  Example