ZUNGBR - generate one of the complex unitary matrices Q or
       P**H determined by ZGEBRD when reducing a complex matrix A
       to bidiagonal form


SYNOPSIS

       SUBROUTINE ZUNGBR( VECT,  M,  N,  K,  A,  LDA,  TAU, WORK,
                          LWORK, INFO )

           CHARACTER      VECT

           INTEGER        INFO, K, LDA, LWORK, M, N

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

       ZUNGBR generates one of the complex unitary matrices Q  or
       P**H determined by ZGEBRD when reducing a complex matrix A
       to bidiagonal form: A = Q * B  *  P**H.  Q  and  P**H  are
       defined  as products of elementary reflectors H(i) or G(i)
       respectively.

       If VECT = 'Q', A is assumed to have been an M-by-K matrix,
       and Q is of order M:
       if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the
       first n columns of Q, where m >= n >= k;
       if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns  Q
       as an M-by-M matrix.

       If  VECT = 'P', A is assumed to have been a K-by-N matrix,
       and P**H is of order N:
       if k < n, P**H = G(k) . . . G(2) G(1) and  ZUNGBR  returns
       the first m rows of P**H, where n >= m >= k;
       if  k  >=  n,  P**H  =  G(n-1)  . . . G(2) G(1) and ZUNGBR
       returns P**H as an N-by-N matrix.


ARGUMENTS

       VECT    (input) CHARACTER*1
               Specifies whether the matrix Q or the matrix  P**H
               is  required,  as  defined  in  the transformation
               applied by ZGEBRD:
               = 'Q':  generate Q;
               = 'P':  generate P**H.

       M       (input) INTEGER
               The number of rows of the matrix Q or P**H  to  be
               returned.  M >= 0.

       N       (input) INTEGER
               The  number  of columns of the matrix Q or P**H to
               be returned.  N >= 0.  If VECT = 'Q', M  >=  N  >=
               min(M,K); if VECT = 'P', N >= M >= min(N,K).

               If VECT = 'Q', the number of columns in the origi­
               nal M-by-K matrix reduced by ZGEBRD.   If  VECT  =
               'P',  the  number  of  rows in the original K-by-N
               matrix reduced by ZGEBRD.  K >= 0.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On  entry, the vectors which define the elementary
               reflectors, as returned by ZGEBRD.  On  exit,  the
               M-by-N matrix Q or P**H.

       LDA     (input) INTEGER
               The leading dimension of the array A. LDA >= M.

       TAU     (input) COMPLEX*16 array, dimension
               (min(M,K))  if VECT = 'Q' (min(N,K)) if VECT = 'P'
               TAU(i) must contain the scalar factor of the  ele­
               mentary reflector H(i) or G(i), which determines Q
               or P**H, as returned by ZGEBRD in its array  argu­
               ment TAUQ or TAUP.

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

       LWORK   (input) INTEGER
               The   dimension   of  the  array  WORK.  LWORK  >=
               max(1,min(M,N)).  For optimum performance LWORK >=
               min(M,N)*NB, where NB is the optimal blocksize.

               If  LWORK = -1, then a workspace query is assumed;
               the routine only calculates the  optimal  size  of
               the  WORK  array,  returns this value as the first
               entry of the WORK  array,  and  no  error  message
               related to LWORK is issued by XERBLA.

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


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