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NAME
     slaein - 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 SLAEIN( RIGHTV, NOINIT, N, H, LDH,  WR,  WI,  VR,
               VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

     LOGICAL NOINIT, RIGHTV

     INTEGER INFO, LDB, LDH, N

     REAL BIGNUM, EPS3, SMLNUM, WI, WR

     REAL B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )



     #include <sunperf.h>

     void slaein(int rightv, int noinit, int  n,  float  *h,  int
               ldh,  float  wr,  float  wi, float *vr, float *vi,
               float *sb, int  ldb,  float  eps3,  float  smlnum,
               float bignum, int *info) ;

PURPOSE
     SLAEIN 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) REAL 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) REAL
               WI      (input) REAL The real and imaginary  parts
               of  the  eigenvalue of H whose corresponding right
               or left eigenvector is to be computed.

     VR        (input/output) REAL array, dimension (N)
               VI      (input/output) REAL 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  eigenvector; if
               WI.ne.0.0 (complex eigenvalue), VR and VI  contain
               the  real and imaginary parts of the computed com-
               plex eigenvector. The eigenvector is normalized so
               that the component of largest magnitude has magni-
               tude 1; here the magnitude  of  a  complex  number
               (x,y)  is taken to be |x| + |y|.  VI is not refer-
               enced if WI = 0.0.

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

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

     WORK      (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.

     BIGNUM    (input) REAL
               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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