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NAME

        ZGEBAK  -  form  the  right  or  left eigenvectors of a complex general
        matrix by backward transformation on the computed eigenvectors  of  the
        balanced matrix output by ZGEBAL
 

SYNOPSIS

        SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )
 
            CHARACTER      JOB, SIDE
 
            INTEGER        IHI, ILO, INFO, LDV, M, N
 
            DOUBLE         PRECISION SCALE( * )
 
            COMPLEX*16     V( LDV, * )
 

PURPOSE

        ZGEBAK forms the right or left eigenvectors of a complex general matrix
        by backward transformation on the computed eigenvectors of the balanced
        matrix output by ZGEBAL.
 

ARGUMENTS

        JOB     (input) CHARACTER*1
                Specifies  the type of backward transformation required: = ’N’,
                do nothing, return immediately; = ’P’, do backward  transforma‐
                tion  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 ZGEBAL.
 
        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
                ZGEBAL.   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
                ZGEBAL.
 
        M       (input) INTEGER
                The number of columns of the matrix V.  M >= 0.
 
        V       (input/output) COMPLEX*16 array, dimension (LDV,M)
                On entry, the matrix of right or left eigenvectors to be trans‐
                formed, as returned by ZHSEIN or ZTREVC.  On exit, V  is  over‐
                written 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.
 

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