NAME

DGEBAK - form 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 i-th argument had an illegal value.

  —  LAPACK version 2.0  —  08 October 1994