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RedHat 9 (Linux i386) - man page for slaein (redhat section l)

SLAEIN(l)					)					SLAEIN(l)

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( * )

PURPOSE
       SLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the ei-
       genvalue (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 complex eigenvector. The eigenvector is normalized so that the compo-
	       nent  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) 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.

LAPACK version 3.0			   15 June 2000 				SLAEIN(l)


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