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

SLAHQR(l)					)					SLAHQR(l)

NAME
       SLAHQR  -  i  an  auxiliary  routine  called by SHSEQR to update the eigenvalues and Schur
       decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows
       and columns ILO to IHI

SYNOPSIS
       SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO )

	   LOGICAL	  WANTT, WANTZ

	   INTEGER	  IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N

	   REAL 	  H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )

PURPOSE
       SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decom-
       position already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows  and
       columns ILO to IHI.

ARGUMENTS
       WANTT   (input) LOGICAL
	       = .TRUE. : the full Schur form T is required;
	       = .FALSE.: only eigenvalues are required.

       WANTZ   (input) LOGICAL
	       = .TRUE. : the matrix of Schur vectors Z is required;
	       = .FALSE.: Schur vectors are not required.

       N       (input) INTEGER
	       The order of the matrix H.  N >= 0.

       ILO     (input) INTEGER
	       IHI	(input) INTEGER It is assumed that H is already upper quasi-triangular in
	       rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR works
	       primarily  with	the  Hessenberg  submatrix  in	rows  and columns ILO to IHI, but
	       applies transformations to all of H if WANTT is .TRUE..	1 <= ILO  <=  max(1,IHI);
	       IHI <= N.

       H       (input/output) REAL array, dimension (LDH,N)
	       On  entry, the upper Hessenberg matrix H.  On exit, if WANTT is .TRUE., H is upper
	       quasi-triangular in rows and columns ILO:IHI, with any 2-by-2 diagonal  blocks  in
	       standard form. If WANTT is .FALSE., the contents of H are unspecified on exit.

       LDH     (input) INTEGER
	       The leading dimension of the array H. LDH >= max(1,N).

       WR      (output) REAL array, dimension (N)
	       WI	(output)  REAL array, dimension (N) The real and imaginary parts, respec-
	       tively, of the computed eigenvalues ILO to IHI are  stored  in  the  corresponding
	       elements  of  WR  and  WI.  If two eigenvalues are computed as a complex conjugate
	       pair, they are stored in consecutive elements of WR  and  WI,  say  the	i-th  and
	       (i+1)th,  with  WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the eigenvalues are
	       stored in the same order as on the diagonal of the Schur form returned in H,  with
	       WR(i)  =  H(i,i),  and,	if  H(i:i+1,i:i+1)  is	a  2-by-2 diagonal block, WI(i) =
	       sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).

       ILOZ    (input) INTEGER
	       IHIZ    (input) INTEGER Specify the rows of Z to  which	transformations  must  be
	       applied if WANTZ is .TRUE..  1 <= ILOZ <= ILO; IHI <= IHIZ <= N.

       Z       (input/output) REAL array, dimension (LDZ,N)
	       If  WANTZ  is  .TRUE., on entry Z must contain the current matrix Z of transforma-
	       tions accumulated by SHSEQR, and on exit Z has been updated;  transformations  are
	       applied only to the submatrix Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is .FALSE., Z is not
	       referenced.

       LDZ     (input) INTEGER
	       The leading dimension of the array Z. LDZ >= max(1,N).

       INFO    (output) INTEGER
	       = 0: successful exit
	       > 0: SLAHQR failed to compute all the  eigenvalues  ILO	to  IHI  in  a	total  of
	       30*(IHI-ILO+1)  iterations;  if	INFO  =  i, elements i+1:ihi of WR and WI contain
	       those eigenvalues which have been successfully computed.

FURTHER DETAILS
       2-96 Based on modifications by
	  David Day, Sandia National Laboratory, USA

LAPACK version 3.0			   15 June 2000 				SLAHQR(l)


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