NAG Library Routine Document

F08WJF (DGGBAK)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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 parameter JOB as supplied to F08WHF (DGGBAL).

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

2:     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:     N – INTEGERInput

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

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

4:     ILO – INTEGERInput

5:     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:     LSCALE($*$) – 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:     RSCALE($*$) – 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:     M – INTEGERInput

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

Constraint: $0\le \mathbf{M}\le \mathbf{N}$.

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

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

On entry: the matrix of right or left eigenvectors, as returned by F08WHF (DGGBAL).

On exit: the transformed right or left eigenvectors.

10:   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:   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  Further Comments

9  Example