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 gen
eral 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 scal
ing 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
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 ille
gal value.
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