redhat man page for dlahqr

DLAHQR(l)								 )								 DLAHQR(l)

NAME
       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

SYNOPSIS
       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, * )

PURPOSE
       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  transforma-
	       tions 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  ei-
	       genvalues  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

LAPACK version 3.0						   15 June 2000 							 DLAHQR(l)