# 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

Univ. of Colorado Denver

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