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CLAHQR(l)			       )			     CLAHQR(l)

NAME
       CLAHQR  -  i an auxiliary routine called by CHSEQR to update the eigen‐
       values 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 eigenval‐
       ues 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 transfor‐
	       mations 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	corre‐
	       sponding 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 trans‐
	       formations 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	refer‐
	       enced.

       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 success‐
	       fully computed.

LAPACK version 3.0		 15 June 2000			     CLAHQR(l)
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