NAME¶

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

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.