CXML
        	    
LAPACK version 3.0
clahqr(3)

PURPOSE
  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

SYNTAX
  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, * )

DESCRIPTION
  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.