---
name: "dggbak"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dggbak/3lapack"
---

# dggbak(3lapack)

forms the right or left eigenvectors of a real generalized eigenvalue problem A\*x = lambda\*B\*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL

## NAME

DGGBAK - forms the right or left eigenvectors of a real generalized eigenvalue problem A\*x = lambda\*B\*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL

## SYNOPSIS

- SUBROUTINE DGGBAK(

  JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO )

- CHARACTER

  JOB, SIDE

- INTEGER

  IHI, ILO, INFO, LDV, M, N

- DOUBLE

  PRECISION LSCALE( \* ), RSCALE( \* ), V( LDV, \* )

## PURPOSE

DGGBAK forms the right or left eigenvectors of a real generalized eigenvalue problem A\*x = lambda\*B\*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL.

## ARGUMENTS

- JOB (input) CHARACTER\*1

  Specifies the type of backward transformation required:\
   \= 'N':  do nothing, return immediately;\
   \= 'P':  do backward transformation for permutation only;\
   \= 'S':  do backward transformation for scaling only;\
   \= 'B':  do backward transformations for both permutation and scaling. JOB must be the same as the argument JOB supplied to DGGBAL.

- SIDE (input) CHARACTER\*1

  \= 'R':  V contains right eigenvectors;\
   \= 'L':  V contains left eigenvectors.

- N (input) INTEGER

  The number of rows of the matrix V.  N \>= 0.

- ILO (input) INTEGER

  IHI     (input) INTEGER The integers ILO and IHI determined by DGGBAL. 1 \<= ILO \<= IHI \<= N, if N \> 0; ILO=1 and IHI=0, if N=0.

- LSCALE (input) DOUBLE PRECISION array, dimension (N)

  Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by DGGBAL.

- RSCALE (input) DOUBLE PRECISION array, dimension (N)

  Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by DGGBAL.

- M (input) INTEGER

  The number of columns of the matrix V.  M \>= 0.

- V (input/output) DOUBLE PRECISION array, dimension (LDV,M)

  On entry, the matrix of right or left eigenvectors to be transformed, as returned by DTGEVC. On exit, V is overwritten by the transformed eigenvectors.

- LDV (input) INTEGER

  The leading dimension of the matrix V. LDV \>= max(1,N).

- INFO (output) INTEGER

  \= 0:  successful exit.\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.

## FURTHER DETAILS

See R.C. Ward, Balancing the generalized eigenvalue problem,\
                SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.