ZLAHQR is an auxiliary routine called by CHSEQR to update the
    eigenvalues and Schur decomposition already computed by CHSEQR, by
    dealing with the Hessenberg submatrix in rows and columns ILO to
    IHI.

WANTT

          WANTT is LOGICAL
          = .TRUE. : the full Schur form T is required;
          = .FALSE.: only eigenvalues are required.

WANTZ

          WANTZ is LOGICAL
          = .TRUE. : the matrix of Schur vectors Z is required;
          = .FALSE.: Schur vectors are not required.

N

          N is INTEGER
          The order of the matrix H.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is 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

          H is COMPLEX*16 array, dimension (LDH,N)
          On entry, the upper Hessenberg matrix H.
          On exit, if INFO is zero and if WANTT is .TRUE., then H
          is upper triangular in rows and columns ILO:IHI.  If INFO
          is zero and if WANTT is .FALSE., then the contents of H
          are unspecified on exit.  The output state of H in case
          INF is positive is below under the description of INFO.

LDH

          LDH is INTEGER
          The leading dimension of the array H. LDH >= max(1,N).

W

          W is 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

          ILOZ is INTEGER

IHIZ

          IHIZ is INTEGER
          Specify the rows of Z to which transformations must be
          applied if WANTZ is .TRUE..
          1 <= ILOZ <= ILO; IHI <= IHIZ <= N.

Z

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

          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= max(1,N).

INFO

          INFO is INTEGER
           = 0:   successful exit
           > 0:   if INFO = i, ZLAHQR failed to compute all the
                  eigenvalues ILO to IHI in a total of 30 iterations
                  per eigenvalue; elements i+1:ihi of W contain
                  those eigenvalues which have been successfully
                  computed.
                  If INFO > 0 and WANTT is .FALSE., then on exit,
                  the remaining unconverged eigenvalues are the
                  eigenvalues of the upper Hessenberg matrix
                  rows and columns ILO through INFO of the final,
                  output value of H.
                  If INFO > 0 and WANTT is .TRUE., then on exit
          (*)       (initial value of H)*U  = U*(final value of H)
                  where U is an orthogonal matrix.    The final
                  value of H is upper Hessenberg and triangular in
                  rows and columns INFO+1 through IHI.
                  If INFO > 0 and WANTZ is .TRUE., then on exit
                      (final value of Z)  = (initial value of Z)*U
                  where U is the orthogonal matrix in (*)
                  (regardless of the value of WANTT.)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

     02-96 Based on modifications by
     David Day, Sandia National Laboratory, USA
     12-04 Further modifications by
     Ralph Byers, University of Kansas, USA
     This is a modified version of ZLAHQR from LAPACK version 3.0.
     It is (1) more robust against overflow and underflow and
     (2) adopts the more conservative Ahues & Tisseur stopping
     criterion (LAWN 122, 1997).