DGEBAK(3)
forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
SYNOPSIS
 SUBROUTINE DGEBAK(

JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
INFO )

CHARACTER
JOB, SIDE

INTEGER
IHI, ILO, INFO, LDV, M, N

DOUBLE
PRECISION SCALE( * ), V( LDV, * )
PURPOSE
DGEBAK forms the right or left eigenvectors of a real general matrix
by backward transformation on the computed eigenvectors of the
balanced matrix output by DGEBAL.
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 DGEBAL.
 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 DGEBAL.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
 SCALE (input) DOUBLE PRECISION array, dimension (N)

Details of the permutation and scaling factors, as returned
by DGEBAL.
 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 DHSEIN or DTREVC.
On exit, V is overwritten by the transformed eigenvectors.
 LDV (input) INTEGER

The leading dimension of the array V. LDV >= max(1,N).
 INFO (output) INTEGER

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