ZLAEIN  -  use  inverse  iteration to find a right or left
       eigenvector corresponding to the eigenvalue W of a complex
       upper Hessenberg matrix H
SYNOPSIS
       SUBROUTINE ZLAEIN( RIGHTV,  NOINIT,  N,  H,  LDH, W, V, B,
                          LDB, RWORK, EPS3, SMLNUM, INFO )
           LOGICAL        NOINIT, RIGHTV
           INTEGER        INFO, LDB, LDH, N
           DOUBLE         PRECISION EPS3, SMLNUM
           COMPLEX*16     W
           DOUBLE         PRECISION RWORK( * )
           COMPLEX*16     B( LDB, * ), H( LDH, * ), V( * )
PURPOSE
       ZLAEIN uses inverse iteration to  find  a  right  or  left
       eigenvector corresponding to the eigenvalue W of a complex
       upper Hessenberg matrix H.
ARGUMENTS
       RIGHTV   (input) LOGICAL
                = .TRUE. : compute right eigenvector;
                = .FALSE.: compute left eigenvector.
       NOINIT   (input) LOGICAL
                = .TRUE. : no initial vector supplied in V
                = .FALSE.: initial vector supplied in V.
       N       (input) INTEGER
               The order of the matrix H.  N >= 0.
       H       (input) COMPLEX*16 array, dimension (LDH,N)
               The upper Hessenberg matrix H.
       LDH     (input) INTEGER
               The leading dimension of  the  array  H.   LDH  >=
               max(1,N).
       W       (input) COMPLEX*16
               The  eigenvalue  of H whose corresponding right or
               left eigenvector is to be computed.
       V       (input/output) COMPLEX*16 array, dimension (N)
               On entry, if NOINIT = .FALSE., V  must  contain  a
               starting vector for inverse iteration; otherwise V
               need not be set.  On exit, V contains the computed
               eigenvector,  normalized  so that the component of
               tude  of a complex number (x,y) is taken to be |x|
               + |y|.
       B       (workspace) COMPLEX*16 array, dimension (LDB,N)
       LDB     (input) INTEGER
               The leading dimension of  the  array  B.   LDB  >=
               max(1,N).
       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
       EPS3    (input) DOUBLE PRECISION
               A  small  machine-dependent value which is used to
               perturb close eigenvalues,  and  to  replace  zero
               pivots.
       SMLNUM  (input) DOUBLE PRECISION
               A  machine-dependent  value close to the underflow
               threshold.
       INFO    (output) INTEGER
               = 0:  successful exit
               = 1:  inverse iteration did not converge; V is set
               to the last iterate.
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