NAG Library Routine Document

f12fcf (real_symm_proc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{nconv}$ – IntegerOutput

On exit: the number of converged eigenvalues as found by f12fbf.

2:     $\mathbf{d}\left(*\right)$ – Real (Kind=nag_wp) arrayOutput

Note: the dimension of the array d must be at least $\mathbf{ncv}$ (see f12faf).

On exit: the first nconv locations of the array d contain the converged approximate eigenvalues.

3:     $\mathbf{z}\left(\mathbf{ldz},*\right)$ – Real (Kind=nag_wp) arrayOutput

Note: the second dimension of the array z must be at least $\mathbf{ncv}$ 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 f12faf).

On exit: if the default option $\mathbf{Vectors}=\mathrm{RITZ}$ (see f12fdf) has been selected then z contains the final set of eigenvectors corresponding to the eigenvalues held in d. The real eigenvector associated with an eigenvalue is stored in the corresponding column of z.

4:     $\mathbf{ldz}$ – IntegerInput

On entry: the first dimension of the array z as declared in the (sub)program from which f12fcf 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, $\mathbf{ldz}\ge 1$.

5:     $\mathbf{sigma}$ – Real (Kind=nag_wp)Input

On entry: if one of the Shifted Inverse (see f12fdf) modes has been selected then sigma contains the real shift used; otherwise sigma is not referenced.

6:     $\mathbf{resid}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array resid must be at least $\mathbf{n}$ (see f12faf).

On entry: must not be modified following a call to f12fbf since it contains data required by f12fcf.

7:     $\mathbf{v}\left(\mathbf{ldv},*\right)$ – 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 f12faf).

On entry: the ncv columns of v contain the Lanczos basis vectors for $\mathrm{OP}$ as constructed by f12fbf.

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.

8:     $\mathbf{ldv}$ – IntegerInput

On entry: the first dimension of the array v as declared in the (sub)program from which f12fcf is called.

Constraint: $\mathbf{ldv}\ge \mathbf{n}$.

9:     $\mathbf{comm}\left(*\right)$ – Real (Kind=nag_wp) arrayCommunication Array

Note: the dimension of the array comm must be at least $\max \left(1,\mathbf{lcomm}\right)$ (see f12faf).

On initial entry: must remain unchanged from the prior call to f12faf.

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

10:   $\mathbf{icomm}\left(*\right)$ – Integer arrayCommunication Array

Note: the dimension of the array icomm must be at least $\max \left(1,\mathbf{licomm}\right)$ (see f12faf).

On initial entry: must remain unchanged from the prior call to f12faf.

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

11:   $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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, $\mathbf{ldz}<\max \left(1,\mathbf{n}\right)$ 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 f12fcf, as communicated through the argument icomm, is zero.

$\mathbf{ifail}=4$

The number of converged eigenvalues as calculated by f12fbf differ from the value passed to it through the argument icomm.

$\mathbf{ifail}=5$

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

$\mathbf{ifail}=8$

Either the routine was called out of sequence (following an initial call to the setup routine and following completion of calls to the reverse communication routine) or the communication arrays have become corrupted.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f12fcfe.f90)

10.2

Program Data

Program Data (f12fcfe.d)

10.3

Program Results

Program Results (f12fcfe.r)