NAG Library Routine Document

f08wjf  (dggbak)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{job}$ – Character(1)Input

On entry: specifies the backward transformation step required.

$\mathbf{job}=\text{'N'}$

No transformations are done.

$\mathbf{job}=\text{'P'}$

Only do backward transformations based on permutations.

$\mathbf{job}=\text{'S'}$

Only do backward transformations based on scaling.

$\mathbf{job}=\text{'B'}$

Do backward transformations for both permutations and scaling.

Note:  this must be the same argument job as supplied to f08whf (dggbal).

Constraint: $\mathbf{job}=\text{'N'}$, $\text{'P'}$, $\text{'S'}$ or $\text{'B'}$.

2:     $\mathbf{side}$ – Character(1)Input

On entry: indicates whether left or right eigenvectors are to be transformed.

$\mathbf{side}=\text{'L'}$

The left eigenvectors are transformed.

$\mathbf{side}=\text{'R'}$

The right eigenvectors are transformed.

Constraint: $\mathbf{side}=\text{'L'}$ or $\text{'R'}$.

3:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrices $A$ and $B$ of the generalized eigenvalue problem.

Constraint: $\mathbf{n}\ge 0$.

4:     $\mathbf{ilo}$ – IntegerInput

5:     $\mathbf{ihi}$ – IntegerInput

On entry: $i_{\mathrm{lo}}$ and $i_{\mathrm{hi}}$ as determined by a previous call to f08whf (dggbal).

Constraints:

• if $\mathbf{n}>0$, $1\le \mathbf{ilo}\le \mathbf{ihi}\le \mathbf{n}$;
• if $\mathbf{n}=0$, $\mathbf{ilo}=1$ and $\mathbf{ihi}=0$.

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

Note: the dimension of the array lscale must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: details of the permutations and scaling factors applied to the left side of the matrices $A$ and $B$, as returned by a previous call to f08whf (dggbal).

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

Note: the dimension of the array rscale must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: details of the permutations and scaling factors applied to the right side of the matrices $A$ and $B$, as returned by a previous call to f08whf (dggbal).

8:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the required number of left or right eigenvectors.

Constraint: $0\le \mathbf{m}\le \mathbf{n}$.

9:     $\mathbf{v}\left(\mathbf{ldv},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

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

On entry: the matrix of right or left eigenvectors, as returned by f08whf (dggbal).

On exit: the transformed right or left eigenvectors.

10:   $\mathbf{ldv}$ – IntegerInput

On entry: the first dimension of the array v as declared in the (sub)program from which f08wjf (dggbak) is called.

Constraint: $\mathbf{ldv}\ge \max \left(1,\mathbf{n}\right)$.

11:   $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example