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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, * )



     #include <sunperf.h>

     void zlahqr(int wantt, int wantz, int n, int ilo,  int  ihi,
               doublecomplex  *h,  int ldh, doublecomplex *w, int
               iloz, int ihiz, doublecomplex *zz,  int  ldz,  int
               *info) ;

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;  transfor-
               mations   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.

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