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NAME
     zgghrd - reduce a pair of complex matrices (A,B) to general-
     ized  upper  Hessenberg  form using unitary transformations,
     where A is a general matrix and B is upper triangular

SYNOPSIS
     SUBROUTINE ZGGHRD( COMPQ, COMPZ, N, ILO,  IHI,  A,  LDA,  B,
               LDB, Q, LDQ, Z, LDZ, INFO )

     CHARACTER COMPQ, COMPZ

     INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N

     COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ,  *
               )



     #include <sunperf.h>

     void zgghrd(char compq, char compz, int n, int ilo, int ihi,
               doublecomplex *za, int lda, doublecomplex *zb, int
               ldb, doublecomplex *q, int ldq, doublecomplex *zz,
               int ldz, int *info) ;

PURPOSE
     ZGGHRD reduces a pair of complex matrices (A,B) to  general-
     ized  upper  Hessenberg  form using unitary transformations,
     where A is a general matrix and B is upper triangular:  Q' *
     A * Z = H and Q' * B * Z = T, where H is upper Hessenberg, T
     is upper triangular, and Q and Z are unitary,  and  '  means
     conjugate transpose.

     The unitary matrices Q and Z are determined as  products  of
     Givens  rotations.  They may either be formed explicitly, or
     they may be postmultiplied into input matrices Q1 and Z1, so
     that

          Q1 * A * Z1' = (Q1*Q) * H * (Z1*Z)'
          Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'


ARGUMENTS
     COMPQ     (input) CHARACTER*1
               = 'N': do not compute Q;
               = 'I': Q is initialized to the  unit  matrix,  and
               the  unitary  matrix  Q is returned; = 'V': Q must
               contain a unitary matrix Q1 on entry, and the pro-
               duct Q1*Q is returned.

     COMPZ     (input) CHARACTER*1
               = 'N': do not compute Q;
               = 'I': Q is initialized to the  unit  matrix,  and
               the  unitary  matrix  Q is returned; = 'V': Q must
               contain a unitary matrix Q1 on entry, and the pro-
               duct Q1*Q is returned.

     N         (input) INTEGER
               The order of the matrices A and B.  N >= 0.

     ILO       (input) INTEGER
               IHI     (input) INTEGER It is assumed  that  A  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  ZGGBAL;  otherwise they
               should be set to 1 and N respectively.  1  <=  ILO
               <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

     A         (input/output) COMPLEX*16 array,  dimension  (LDA,
               N)
               On entry, the N-by-N general matrix to be reduced.
               On exit, the upper triangle and the first subdiag-
               onal of A are overwritten with the  upper  Hessen-
               berg matrix H, and the rest is set to zero.

     LDA       (input) INTEGER
               The leading dimension of  the  array  A.   LDA  >=
               max(1,N).

     B         (input/output) COMPLEX*16 array,  dimension  (LDB,
               N)
               On entry, the N-by-N upper  triangular  matrix  B.
               On  exit,  the upper triangular matrix T = Q' B Z.
               The elements below the diagonal are set to zero.

     LDB       (input) INTEGER
               The leading dimension of  the  array  B.   LDB  >=
               max(1,N).

     Q         (input/output) COMPLEX*16 array,  dimension  (LDQ,
               N)
               If COMPQ='N':  Q is not referenced.
               If COMPQ='I':  on entry, Q need not be set, and on
               exit it contains the unitary matrix Q, where Q' is
               the product of the  Givens  transformations  which
               are applied to A and B on the left.  If COMPQ='V':
               on entry, Q must contain a unitary matrix Q1,  and
               on exit this is overwritten by Q1*Q.

     LDQ       (input) INTEGER
               The leading dimension of the array Q.  LDQ >= N if
               COMPQ='V' or 'I'; LDQ >= 1 otherwise.

     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  it  contains  the unitary matrix Z, which is
               the product of the  Givens  transformations  which
               are   applied  to  A  and  B  on  the  right.   If
               COMPZ='V':  on entry, Z  must  contain  a  unitary
               matrix  Z1,  and  on  exit  this is overwritten by
               Z1*Z.

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

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.

FURTHER DETAILS
     This routine reduces A to Hessenberg  and  B  to  triangular
     form   by   an   unblocked   reduction,   as   described  in
     _Matrix_Computations_, by Golub and van Loan (Johns  Hopkins
     Press).

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