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claein

 NAME
      CLAEIN - use inverse iteration to find a right or left
      eigenvector corresponding to the eigenvalue W of a complex
      upper Hessenberg matrix H

 SYNOPSIS
      SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB,
                         RWORK, EPS3, SMLNUM, INFO )

          LOGICAL        NOINIT, RIGHTV

          INTEGER        INFO, LDB, LDH, N

          REAL           EPS3, SMLNUM

          COMPLEX        W

          REAL           RWORK( * )

          COMPLEX        B( LDB, * ), H( LDH, * ), V( * )

 PURPOSE
      CLAEIN uses inverse iteration to find a right or left eigen-
      vector 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 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
              The eigenvalue of H whose corresponding right or
              left eigenvector is to be computed.

      V       (input/output) COMPLEX 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
              largest magnitude has magnitude 1; here the magni-
              tude of a complex number (x,y) is taken to be |x| +
              |y|.

      B       (workspace) COMPLEX array, dimension (LDB,N)

      LDB     (input) INTEGER
              The leading dimension of the array B.  LDB >=
              max(1,N).

      RWORK   (workspace) REAL array, dimension (N)

      EPS3    (input) REAL
              A small machine-dependent value which is used to
              perturb close eigenvalues, and to replace zero
              pivots.

      SMLNUM  (input) REAL
              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.