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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, * )



     #include <sunperf.h>

     void dlahqr(int wantt, int wantz, int n, int ilo,  int  ihi,
               double  *h,  int  ldh, double *wr, double *wi, int
               iloz, int ihiz, double *dz, int ldz, int *info) ;

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 eigen-
               values 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;  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: DLAHQR failed to compute all the  eigenvalues
               ILO  to  IHI  in  a total of 30*(IHI-ILO+1) itera-
               tions; if INFO = i, elements i+1:ihi of WR and  WI
               contain those eigenvalues which have been success-
               fully computed.

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