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SLAEIN(3F)							    SLAEIN(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

     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    [Toc]    [Back]

     SLAEIN uses inverse iteration to find a right or left eigenvector
     corresponding to the eigenvalue (WR,WI) of	a real upper Hessenberg	matrix
     H.

ARGUMENTS    [Toc]    [Back]

     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



									Page 1






SLAEIN(3F)							    SLAEIN(3F)



	     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) 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.
SLAEIN(3F)							    SLAEIN(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

     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    [Toc]    [Back]

     SLAEIN uses inverse iteration to find a right or left eigenvector
     corresponding to the eigenvalue (WR,WI) of	a real upper Hessenberg	matrix
     H.

ARGUMENTS    [Toc]    [Back]

     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



									Page 1






SLAEIN(3F)							    SLAEIN(3F)



	     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) 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.


									PPPPaaaaggggeeee 2222
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