NAG Library Function Document

nag_dggbak (f08wjc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     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:     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:     n – IntegerInput

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

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

5:     ilo – IntegerInput

6:     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:     lscale[$\mathit{dim}$] – 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:     rscale[$\mathit{dim}$] – 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:     m – IntegerInput

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

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

10:   v[$\mathit{dim}$] – 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:   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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

7  Accuracy

8  Further Comments

9  Example