CLAHQR(l)								 )								 CLAHQR(l)

NAME

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

SYNOPSIS

       SUBROUTINE CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO )

	   LOGICAL	  WANTT, WANTZ

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

	   COMPLEX	  H( LDH, * ), W( * ), Z( LDZ, * )

PURPOSE

       CLAHQR is an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by  CHSEQR,  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 triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0
	       (unless ILO = 1).  CLAHQR 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) COMPLEX array, dimension (LDH,N)
	       On  entry, the upper Hessenberg matrix H.  On exit, if WANTT is .TRUE., H is upper 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).

       W       (output) COMPLEX array, dimension (N)
	       The computed eigenvalues ILO to IHI are stored in the corresponding elements of W. If WANTT is .TRUE., the eigenvalues  are  stored
	       in the same order as on the diagonal of the Schur form returned in H, with W(i) = H(i,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) COMPLEX array, dimension (LDZ,N)
	       If WANTZ is .TRUE., on entry Z must contain the current matrix Z of transformations accumulated by CHSEQR, 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: if INFO = i, CLAHQR failed to compute all the eigenvalues ILO to IHI in a total of 30*(IHI-ILO+1) iterations; elements i+1:ihi
	       of W contain those eigenvalues which have been successfully computed.

LAPACK version 3.0						   15 June 2000 							 CLAHQR(l)