# ?ggbak

Forms the right or left eigenvectors of a generalized eigenvalue problem.

## Syntax

FORTRAN 77:

call sggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

call dggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

call cggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

call zggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)

Fortran 95:

call ggbak(v [, ilo] [,ihi] [,lscale] [,rscale] [,job] [,info])

## Description

This routine forms the right or left eigenvectors of a real/complex generalized eigenvalue problem

`A*x = λ*B*x`

by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ?ggbal.

## Input Parameters

job

  CHARACTER*1. Specifies the type of backward transformation required. Must be 'N', 'P', 'S', or 'B'.

  If `job = 'N'`, then no operations are done; return.

  If `job = 'P'`, then do backward transformation for permutation only.

  If `job = 'S'`, then do backward transformation for scaling only.

  If `job = 'B'`, then do backward transformation for both permutation and scaling. This argument must be the same as the argument job supplied to ?ggbal.

side

  CHARACTER*1. Must be 'L' or 'R'.

  If `side = 'L'` , then v contains left eigenvectors.

  If `side = 'R'` , then v contains right eigenvectors.

n

  INTEGER. The number of rows of the matrix V (n ≥ 0).

ilo, ihi

  INTEGER. The integers ilo and ihi determined by ?gebal. Constraint:

  If `n > 0`, then 1 ≤ ilo ≤ ihi ≤ n;

  if `n = 0`, then `ilo = 1` and `ihi = 0`.

lscale, rscale

  REAL for single precision flavors

  DOUBLE PRECISION for double precision flavors.

  Arrays, DIMENSION at least max(1, n).

  The array lscale contains details of the permutations and/or scaling factors applied to the left side of A and B, as returned by ?ggbal.

  The array rscale contains details of the permutations and/or scaling factors applied to the right side of A and B, as returned by ?ggbal.

m

  INTEGER. The number of columns of the matrix V

  (m ≥ 0).

v

  REAL for sggbak

  DOUBLE PRECISION for dggbak

  COMPLEX for cggbak

  DOUBLE COMPLEX for zggbak.

  Array v(ldv,*). Contains the matrix of right or left eigenvectors to be transformed, as returned by ?tgevc.

  The second dimension of v must be at least max(1, m).

ldv

  INTEGER. The first dimension of v; at least max(1, n).

## Output Parameters

v

  Overwritten by the transformed eigenvectors

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = -i`, the ith parameter had an illegal value.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see Fortran 95 Interface Conventions.

Specific details for the routine ggbak interface are the following:

v

  Holds the matrix V of size (n,m).

lscale

  Holds the vector of length (n).

rscale

  Holds the vector of length (n).

ilo

  Default value for this argument is `ilo = 1`.

ihi

  Default value for this argument is `ihi = n`.

job

  Must be 'B', 'S', 'P', or 'N'. The default value is 'B'.

side

  If omitted, this argument is restored based on the presence of arguments lscale and rscale as follows:

  `side = 'L'`, if lscale is present and rscale omitted,

  `side = 'R'`, if lscale is omitted and rscale present.

  Note that there will be an error condition if both lscale and rscale are present or if they both are omitted.

Parent topic: Generalized Nonsymmetric Eigenvalue Problems