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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( * )



     #include <sunperf.h>

     void claein(int rightv, int noinit, int n, complex  *h,  int
               ldh, complex *w, complex *v, complex *cb, int ldb,
               float eps3, float smlnum, int *info) ;

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.

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