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ZLAHQR2(l)                             )                            ZLAHQR2(l)


NAME

       ZLAHQR2 - i an auxiliary routine called by ZHSEQR to update the
       eigenvalues and Schur decomposition already computed by ZHSEQR, by
       dealing with the Hessenberg submatrix in rows and columns ILO to IHI


SYNOPSIS

       SUBROUTINE ZLAHQR2( 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*16 H( LDH, * ), W( * ), Z( LDZ, * )


PURPOSE

       ZLAHQR2 is an auxiliary routine called by ZHSEQR to update the
       eigenvalues and Schur decomposition already computed by ZHSEQR, by
       dealing with the Hessenberg submatrix in rows and columns ILO to IHI.
       This version of ZLAHQR (not the standard LAPACK version) uses a
         double-shift algorithm (like LAPACK's DLAHQR).
       Unlike the standard LAPACK convention, this does not assume the
         subdiagonal is real, nor does it work to preserve this quality if
         given.


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).  ZLAHQR 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*16 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.  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*16 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*16 array, dimension (LDZ,N)
               If WANTZ is .TRUE., on entry Z must contain the current matrix
               Z of transformations, 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, ZLAHQR 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.


FURTHER DETAILS

       Modified by Mark R. Fahey, June, 2000

ScaLAPACK version 1.7           13 August 2001                      ZLAHQR2(l)

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