NAG Library Function Document

nag_dggbak (f08wjc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{job}$ – Nag_JobTypeInput

On entry: specifies the backward transformation step required.

$\mathbf{job}=\mathrm{Nag\_DoNothing}$

No transformations are done.

$\mathbf{job}=\mathrm{Nag\_Permute}$

Only do backward transformations based on permutations.

$\mathbf{job}=\mathrm{Nag\_Scale}$

Only do backward transformations based on scaling.

$\mathbf{job}=\mathrm{Nag\_DoBoth}$

Do backward transformations for both permutations and scaling.

Note:  this must be the same argument job as supplied to nag_dggbal (f08whc).

Constraint: $\mathbf{job}=\mathrm{Nag\_DoNothing}$, $\mathrm{Nag\_Permute}$, $\mathrm{Nag\_Scale}$ or $\mathrm{Nag\_DoBoth}$.

3:    $\mathbf{side}$ – Nag_SideTypeInput

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

$\mathbf{side}=\mathrm{Nag\_LeftSide}$

The left eigenvectors are transformed.

$\mathbf{side}=\mathrm{Nag\_RightSide}$

The right eigenvectors are transformed.

Constraint: $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$.

4:    $\mathbf{n}$ – IntegerInput

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

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

5:    $\mathbf{ilo}$ – IntegerInput

6:    $\mathbf{ihi}$ – IntegerInput

On entry: $i_{\mathrm{lo}}$ and $i_{\mathrm{hi}}$ as determined by a previous call to nag_dggbal (f08whc).

Constraints:

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

7:    $\mathbf{lscale}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, 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 nag_dggbal (f08whc).

8:    $\mathbf{rscale}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, 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 nag_dggbal (f08whc).

9:    $\mathbf{m}$ – IntegerInput

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

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

10:  $\mathbf{v}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array v must be at least

• $\max \left(1,\mathbf{pdv}\times \mathbf{m}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdv}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $V$ is stored in

• $\mathbf{v}\left[\left(j-1\right)\times \mathbf{pdv}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{v}\left[\left(i-1\right)\times \mathbf{pdv}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the matrix of right or left eigenvectors, as returned by nag_dggbal (f08whc).

On exit: the transformed right or left eigenvectors.

11:  $\mathbf{pdv}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array v.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdv}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdv}\ge \max \left(1,\mathbf{m}\right)$.

12:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{pdv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdv}>0$.

NE_INT_2

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{m}\le \mathbf{n}$.

On entry, $\mathbf{pdv}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdv}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pdv}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdv}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT_3

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$, $\mathbf{ilo}=〈\mathit{\text{value}}〉$ and $\mathbf{ihi}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{n}>0$, $1\le \mathbf{ilo}\le \mathbf{ihi}\le \mathbf{n}$;
if $\mathbf{n}=0$, $\mathbf{ilo}=1$ and $\mathbf{ihi}=0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example