dggbak(3)

NAME

DGGBAK - form 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 gen

eralized eigenvalue problem A*x = lambda*B*x, by backward trans

formation on the computed eigenvectors of the balanced pair of

matrices output by DGGBAL.

ARGUMENTS

JOB (input) CHARACTER*1

Specifies the type of backward transformation re

quired:
= 'N': do nothing, return immediately;
= 'P': do backward transformation for permutation

only;
= 'S': do backward transformation for scaling on

ly;
= 'B': do backward transformations for both per

mutation 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 over

written 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 ille

gal value.

FURTHER DETAILS

See R.C. Ward, Balancing the generalized eigenvalue prob

lem,

SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

LAPACK version 3.0 15 June 2000

DGGBAK(3)