sgebak(3F)

NAME
     SGEBAK - form the right or left eigenvectors of a real general matrix by
     backward transformation on the computed eigenvectors of the balanced
     matrix output by SGEBAL

SYNOPSIS
     SUBROUTINE SGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )

         CHARACTER      JOB, SIDE

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

         REAL           V( LDV, * ), SCALE( * )

PURPOSE
     SGEBAK forms the right or left eigenvectors of a real general matrix by
     backward transformation on the computed eigenvectors of the balanced
     matrix output by SGEBAL.


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 SGEBAL.

     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
             SGEBAL.  1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

     SCALE   (input) REAL array, dimension (N)
             Details of the permutation and scaling factors, as returned by
             SGEBAL.

     M       (input) INTEGER
             The number of columns of the matrix V.  M >= 0.

     V       (input/output) REAL array, dimension (LDV,M)
             On entry, the matrix of right or left eigenvectors to be
             transformed, as returned by SHSEIN or STREVC.  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.