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NAME
     cgbbrd - reduce a complex general m-by-n band  matrix  A  to
     real upper bidiagonal form B by a unitary transformation

SYNOPSIS
     SUBROUTINE CGBBRD(VECT, M, N, NCC, KL, KU, AB, LDAB,  D,  E,
               Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO)

     CHARACTER VECT

     INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

     REAL D( * ), E( * ), RWORK( * )

     COMPLEX AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, *
               ), WORK( * )



     #include <sunperf.h>

     void cgbbrd(char vect, int m, int n, int ncc,  int  kl,  int
               ku,  complex  *cab,  int ldab, float *d, float *e,
               complex *q, int ldq, complex *pt, int  ldpt,  com-
               plex *cc, int ldc, int *info);

PURPOSE
     CGBBRD reduces a complex general m-by-n  band  matrix  A  to
     real upper bidiagonal form B by a unitary transformation: Q'
     * A * P = B.

     The routine computes B, and optionally forms  Q  or  P',  or
     computes Q'*C for a given matrix C.


ARGUMENTS
     VECT      (input) CHARACTER*1
               Specifies whether or not the matrices Q and P' are
               to be formed.  = 'N': do not form Q or P';
               = 'Q': form Q only;
               = 'P': form P' only;
               = 'B': form both.

     M         (input) INTEGER
               The number of rows of the matrix A.  M >= 0.

     N         (input) INTEGER
               The number of columns of the matrix A.  N >= 0.

     NCC       (input) INTEGER
               The number of columns of the matrix C.  NCC >= 0.

     KL        (input) INTEGER
               The number of subdiagonals of the matrix A. KL  >=
               0.

     KU        (input) INTEGER
               The number of superdiagonals of the matrix  A.  KU
               >= 0.

     AB        (input/output) COMPLEX array, dimension (LDAB,N)
               On entry, the m-by-n band matrix A, stored in rows
               1  to  KL+KU+1.  The j-th column of A is stored in
               the j-th  column  of  the  array  AB  as  follows:
               AB(ku+1+i-j,j)     =     A(i,j)    for    max(1,j-
               ku)<=i<=min(m,j+kl).  On exit, A is overwritten by
               values generated during the reduction.

     LDAB      (input) INTEGER
               The leading dimension of  the  array  A.  LDAB  >=
               KL+KU+1.

     D         (output) REAL array, dimension (min(M,N))
               The diagonal elements of the bidiagonal matrix B.

     E         (output) REAL array, dimension (min(M,N)-1)
               The  superdiagonal  elements  of  the   bidiagonal
               matrix B.

     Q         (output) COMPLEX array, dimension (LDQ,M)
               If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.
               If  VECT  =  'N' or 'P', the array Q is not refer-
               enced.

     LDQ       (input) INTEGER
               The leading dimension of  the  array  Q.   LDQ  >=
               max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.

     PT        (output) COMPLEX array, dimension (LDPT,N)
               If VECT = 'P' or 'B', the  n-by-n  unitary  matrix
               P'.   If  VECT  =  'N' or 'Q', the array PT is not
               referenced.

     LDPT      (input) INTEGER
               The leading dimension of the array  PT.   LDPT  >=
               max(1,N)  if  VECT  = 'P' or 'B'; LDPT >= 1 other-
               wise.

     C         (input/output) COMPLEX array, dimension (LDC,NCC)
               On entry, an m-by-ncc matrix C.   On  exit,  C  is
               overwritten by Q'*C.  C is not referenced if NCC =
               0.

     LDC       (input) INTEGER
               The leading dimension of  the  array  C.   LDC  >=
               max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.

     WORK      (workspace) COMPLEX array, dimension (max(M,N))

     RWORK     (workspace) REAL array, dimension (max(M,N))

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

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