# dggbak.f - Man Page

SRC/dggbak.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)

DGGBAK

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.```
Parameters

JOB

```          JOB is 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

```          SIDE is CHARACTER*1
= 'R':  V contains right eigenvectors;
= 'L':  V contains left eigenvectors.```

N

```          N is INTEGER
The number of rows of the matrix V.  N >= 0.```

ILO

`          ILO is INTEGER`

IHI

```          IHI is 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

```          LSCALE is 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

```          RSCALE is 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

```          M is INTEGER
The number of columns of the matrix V.  M >= 0.```

V

```          V is 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

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

INFO

```          INFO is INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Further Details:

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

Definition at line 145 of file dggbak.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dggbak(3) is an alias of dggbak.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK