NAG Library Routine Document

F12ACF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NCONV – INTEGEROutput

On exit: the number of converged eigenvalues as found by F12ABF.

2:     DR($*$) – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array DR must be at least $\mathbf{NEV}$ (see F12AAF).

On exit: the first NCONV locations of the array DR contain the real parts of the converged approximate eigenvalues.

3:     DI($*$) – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array DI must be at least $\mathbf{NEV}$ (see F12AAF).

On exit: the first NCONV locations of the array DI contain the imaginary parts of the converged approximate eigenvalues.

4:     Z(LDZ,$*$) – REAL (KIND=nag_wp) arrayOutput

Note: the second dimension of the array Z must be at least $\mathbf{NEV}+1$ if the default option $\mathbf{Vectors}=\mathrm{RITZ}$ has been selected and at least $1$ if the option $\mathbf{Vectors}=\mathrm{NONE}$ or $\mathrm{SCHUR}$ has been selected (see F12AAF).

On exit: if the default option $\mathbf{Vectors}=\mathrm{RITZ}$ (see F12ADF) has been selected then Z contains the final set of eigenvectors corresponding to the eigenvalues held in DR and DI. The complex eigenvector associated with the eigenvalue with positive imaginary part is stored in two consecutive columns. The first column holds the real part of the eigenvector and the second column holds the imaginary part. The eigenvector associated with the eigenvalue with negative imaginary part is simply the complex conjugate of the eigenvector associated with the positive imaginary part.

5:     LDZ – INTEGERInput

On entry: the first dimension of the array Z as declared in the (sub)program from which F12ACF is called.

Constraints:

• if the default option $\mathbf{Vectors}=\text{Ritz}$ has been selected, $\mathbf{LDZ}\ge \mathbf{N}$;
• if the option $\mathbf{Vectors}=\text{None or Schur}$ has been selected, $\mathbf{LDZ}\ge 1$.

6:     SIGMAR – REAL (KIND=nag_wp)Input

On entry: if one of the Shifted Inverse Real modes have been selected then SIGMAR contains the real part of the shift used; otherwise SIGMAR is not referenced.

7:     SIGMAI – REAL (KIND=nag_wp)Input

On entry: if one of the Shifted Inverse Real modes have been selected then SIGMAI contains the imaginary part of the shift used; otherwise SIGMAI is not referenced.

8:     RESID($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array RESID must be at least $\mathbf{N}$ (see F12AAF).

On entry: must not be modified following a call to F12ABF since it contains data required by F12ACF.

9:     V(LDV,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array V must be at least $\max \left(1,\mathbf{NCV}\right)$ (see F12AAF).

On entry: the NCV columns of V contain the Arnoldi basis vectors for $\mathrm{OP}$ as constructed by F12ABF.

On exit: if the option $\mathbf{Vectors}=\mathrm{SCHUR}$ has been set, or the option $\mathbf{Vectors}=\mathrm{RITZ}$ has been set and a separate array Z has been passed (i.e., Z does not equal V), then the first NCONV columns of V will contain approximate Schur vectors that span the desired invariant subspace.

10:   LDV – INTEGERInput

On entry: the first dimension of the array V as declared in the (sub)program from which F12ACF is called.

Constraint: $\mathbf{LDV}\ge \mathbf{N}$.

11:   COMM($*$) – REAL (KIND=nag_wp) arrayCommunication Array

Note: the dimension of the array COMM must be at least $\max \left(1,\mathbf{LCOMM}\right)$ (see F12AAF).

On initial entry: must remain unchanged from the prior call to F12ABF.

On exit: contains data on the current state of the solution.

12:   ICOMM($*$) – INTEGER arrayCommunication Array

Note: the dimension of the array ICOMM must be at least $\max \left(1,\mathbf{LICOMM}\right)$ (see F12AAF).

On initial entry: must remain unchanged from the prior call to F12ABF.

On exit: contains data on the current state of the solution.

13:   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, $\mathbf{LDZ}<\max \left(1,\mathbf{N}\right)$ or $\mathbf{LDZ}<1$ when no vectors are required.

$\mathbf{IFAIL}=2$

On entry, the option $\mathbf{Vectors}=\text{Select}$ was selected, but this is not yet implemented.

$\mathbf{IFAIL}=3$

The number of eigenvalues found to sufficient accuracy prior to calling F12ACF, as communicated through the parameter ICOMM, is zero.

$\mathbf{IFAIL}=4$

The number of converged eigenvalues as calculated by F12ABF differ from the value passed to it through the parameter ICOMM.

$\mathbf{IFAIL}=5$

Unexpected error during calculation of a real Schur form: there was a failure to compute all the converged eigenvalues. Please contact NAG.

$\mathbf{IFAIL}=6$

Unexpected error: the computed Schur form could not be reordered by an internal call. Please contact NAG.

$\mathbf{IFAIL}=7$

Unexpected error in internal call while calculating eigenvectors. Please contact NAG.

$\mathbf{IFAIL}=8$

Either the solver routine F12ABF has not been called prior to the call of this routine or a communication array has become corrupted.

$\mathbf{IFAIL}=9$

The routine was unable to dynamically allocate sufficient internal workspace. Please contact NAG.

$\mathbf{IFAIL}=10$

An unexpected error has occurred. Please contact NAG.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f12acfe.f90)

9.2  Program Data

Program Data (f12acfe.d)

9.3  Program Results

Program Results (f12acfe.r)