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

SYNOPSIS
     SUBROUTINE SLAHQR( 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

     REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )



     #include <sunperf.h>

     void slahqr(int wantt, int wantz, int n, int ilo,  int  ihi,
               float *h, int ldh, float *wr, float *wi,
                int iloz, int  ihiz,  float  *sz,  int  ldz,  int
               *info) ;

PURPOSE
     SLAHQR is an auxiliary routine called by  SHSEQR  to  update
     the  eigenvalues and Schur decomposition already computed by
     SHSEQR, 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).  SLAHQR  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) REAL 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) REAL array, dimension (N)
               WI      (output) REAL  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 eigen-
               values 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 eigenvalues
               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) REAL array, dimension (LDZ,N)
               If WANTZ is .TRUE., on entry Z  must  contain  the
               current matrix Z of transformations accumulated by
               SHSEQR, 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: SLAHQR 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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