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


SYNOPSIS

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

           CHARACTER      VECT

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

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


PURPOSE

       CUNGBR generates one of the complex unitary matrices Q  or
       P**H determined by CGEBRD 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 CUNGBR returns the
       first n columns of Q, where m >= n >= k;
       if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR 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  CUNGBR  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 CUNGBR
       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 CGEBRD:
               = '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 CGEBRD.   If  VECT  =
               'P',  the  number  of  rows in the original K-by-N
               matrix reduced by CGEBRD.  K >= 0.

       A       (input/output) COMPLEX array, dimension (LDA,N)
               On entry, the vectors which define the  elementary
               reflectors,  as  returned by CGEBRD.  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 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 CGEBRD in its array argu­
               ment TAUQ or TAUP.

       WORK    (workspace/output) COMPLEX 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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