dlahqr(3F)

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 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.