CXML
        	    
LAPACK version 3.0
dlaein(3)

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

SYNTAX
  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( * )

DESCRIPTION
  DLAEIN uses inverse iteration to find a right or left eigenvector
  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 imaginary 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 eigenvector; 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 magnitude has magnitude 1; here the
	  magnitude of a complex 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.