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NAME
     dlaein - use inverse iteration  to  find  a  right  or  left
     eigenvector  corresponding  to  the  eigenvalue (WR,WI) of a
     real upper Hessenberg matrix H

SYNOPSIS
     SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH,  WR,  WI,  VR,
               VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

     LOGICAL NOINIT, RIGHTV

     INTEGER INFO, LDB, LDH, N

     DOUBLE PRECISION BIGNUM, EPS3, SMLNUM, WI, WR

     DOUBLE PRECISION B( LDB, * ), H( LDH, * ), VI( * ), VR( * ),
               WORK( * )



     #include <sunperf.h>

     void dlaein(int rightv, int noinit, int n,  double  *h,  int
               ldh, double wr, double wi, double *vr, double *vi,
               double *db, int ldb, double eps3,  double  smlnum,
               double bignum, int *info) ;

PURPOSE
     DLAEIN uses inverse iteration to find a right or left eigen-
     vector  corresponding  to  the  eigenvalue (WR,WI) of a real
     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 (VR,VI).
               = .FALSE.: initial vector supplied in (VR,VI).

     N         (input) INTEGER
               The order of the matrix H.  N >= 0.

     H         (input) DOUBLE PRECISION array, dimension (LDH,N)
               The upper Hessenberg matrix H.

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

     WR        (input) DOUBLE PRECISION
               WI      (input) DOUBLE PRECISION The real and ima-
               ginary   parts   of  the  eigenvalue  of  H  whose
               corresponding right or left eigenvector is  to  be
               computed.

     VR        (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               VI       (input/output)  DOUBLE  PRECISION  array,
               dimension (N) On entry, if NOINIT = .FALSE. and WI
               = 0.0, VR must contain a real starting vector  for
               inverse iteration using the real eigenvalue WR; if
               NOINIT = .FALSE. and WI.ne.0.0,  VR  and  VI  must
               contain  the real and imaginary parts of a complex
               starting vector for inverse  iteration  using  the
               complex  eigenvalue  (WR,WI);  otherwise VR and VI
               need not be set.  On  exit,  if  WI  =  0.0  (real
               eigenvalue),  VR contains the computed real eigen-
               vector; if WI.ne.0.0 (complex eigenvalue), VR  and
               VI  contain  the  real  and imaginary parts of the
               computed complex eigenvector. The  eigenvector  is
               normalized so that the component of largest magni-
               tude has magnitude 1; here the magnitude of a com-
               plex number (x,y) is taken to be |x| + |y|.  VI is
               not referenced if WI = 0.0.

     B         (workspace)  DOUBLE  PRECISION  array,   dimension
               (LDB,N)

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

     WORK      (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.

     BIGNUM    (input) DOUBLE PRECISION
               A machine-dependent value close  to  the  overflow
               threshold.

     INFO      (output) INTEGER
               = 0:  successful exit
               = 1:  inverse iteration did not  converge;  VR  is
               set   to  the  last  iterate,  and  so  is  VI  if
               WI.ne.0.0.

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