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DLAEIN(3F)							    DLAEIN(3F)

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( * )

PURPOSE
     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

									Page 1

DLAEIN(3F)							    DLAEIN(3F)

	     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.

									Page 2

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