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zlahqr

 NAME
      ZLAHQR - 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 ZLAHQR( 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
      ZLAHQR 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.

 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, 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*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 accumulated by
              ZHSEQR, and on exit Z has been updated; transforma-
              tions 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: ZLAHQR 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 W contain those
              eigenvalues which have been successfully computed.