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NAME
     zhseqr - compute the eigenvalues of a complex upper  Hessen-
     berg  matrix  H,  and, optionally, the matrices T and Z from
     the Schur decomposition H = Z T Z**H, where T  is  an  upper
     triangular  matrix  (the  Schur  form), and Z is the unitary
     matrix of Schur vectors

SYNOPSIS
     SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H,  LDH,  W,  Z,
               LDZ, WORK, LWORK, INFO )

     CHARACTER COMPZ, JOB

     INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N

     COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )



     #include <sunperf.h>

     void zhseqr(char job, char compz, int n, int ilo,  int  ihi,
               doublecomplex *h, int ldh, doublecomplex *w, doub-
               lecomplex *zz, int ldz, int *info);

PURPOSE
     ZHSEQR computes the eigenvalues of a complex  upper  Hessen-
     berg  matrix  H,  and, optionally, the matrices T and Z from
     the Schur decomposition H = Z T Z**H, where T  is  an  upper
     triangular  matrix  (the  Schur  form), and Z is the unitary
     matrix of Schur vectors.

     Optionally Z may be postmultiplied  into  an  input  unitary
     matrix Q, so that this routine can give the Schur factoriza-
     tion of a matrix A which has been reduced to the  Hessenberg
     form   H   by   the  unitary  matrix  Q:   A  =  Q*H*Q**H  =
     (QZ)*T*(QZ)**H.


ARGUMENTS
     JOB       (input) CHARACTER*1
               = 'E': compute eigenvalues only;
               = 'S': compute eigenvalues and the Schur form T.

     COMPZ     (input) CHARACTER*1
               = 'N': no Schur vectors are computed;
               = 'I': Z is initialized to the unit matrix and the
               matrix Z of Schur vectors of H is returned; = 'V':
               Z must contain an unitary matrix Q on  entry,  and
               the product Q*Z is returned.

     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
               1:ILO-1 and IHI+1:N. ILO and IHI are normally  set
               by  a  previous call to ZGEBAL, and then passed to
               CGEHRD when the matrix output by ZGEBAL is reduced
               to  Hessenberg  form. Otherwise ILO and IHI should
               be set to 1 and N respectively.  1 <= ILO  <=  IHI
               <= N, if N > 0; ILO=1 and IHI=0, if N=0.

     H         (input/output) COMPLEX*16 array, dimension (LDH,N)
               On entry, the upper Hessenberg matrix H.  On exit,
               if  JOB  =  'S',  H  contains the upper triangular
               matrix T from the Schur decomposition  (the  Schur
               form).  If  JOB  =  'E',  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. If JOB = 'S', the eigen-
               values  are  stored  in  the  same order as on the
               diagonal of the Schur form  returned  in  H,  with
               W(i) = H(i,i).

     Z         (input/output) COMPLEX*16 array, dimension (LDZ,N)
               If COMPZ = 'N': Z is not referenced.
               If COMPZ = 'I': on entry, Z need not be  set,  and
               on  exit,  Z  contains the unitary matrix Z of the
               Schur vectors of H.  If COMPZ = 'V':  on  entry  Z
               must  contain an N-by-N matrix Q, which is assumed
               to be equal to the unit matrix except for the sub-
               matrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.
               Normally Q is  the  unitary  matrix  generated  by
               ZUNGHR  after  the call to ZGEHRD which formed the
               Hessenberg matrix H.

     LDZ       (input) INTEGER
               The leading dimension of  the  array  Z.   LDZ  >=
               max(1,N)  if  COMPZ  = 'I' or 'V'; LDZ >= 1 other-
               wise.

     WORK      (workspace) COMPLEX*16 array, dimension (N)

     LWORK     (input) INTEGER
               This argument is currently redundant.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, ZHSEQR failed  to  compute  all
               the  eigenvalues  in  a  total  of  30*(IHI-ILO+1)
               iterations; elements 1:ilo-1 and i+1:n of  W  con-
               tain  those  eigenvalues  which have been success-
               fully computed.

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