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LAPACK version 3.0
dlahqr(3)

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

SYNTAX
  SUBROUTINE DLAHQR( 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

      DOUBLE	     PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )

DESCRIPTION
  DLAHQR is an auxiliary routine called by DHSEQR to update the eigenvalues
  and Schur decomposition already computed by DHSEQR, 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). DLAHQR 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)
	  WI	  (output) DOUBLE PRECISION array, dimension (N) The real and
	  imaginary parts, respectively, 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) DOUBLE PRECISION array, dimension (LDZ,N)
	  If WANTZ is .TRUE., on entry Z must contain the current matrix Z of
	  transformations accumulated by DHSEQR, 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: DLAHQR 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