CXML
        	    
LAPACK version 3.0
zungbr(3)

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

SYNTAX
  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( * )

DESCRIPTION
  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).

  K	  (input) INTEGER
	  If VECT = 'Q', the number of columns in the original 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 elementary reflector H(i) or G(i),
	  which determines Q or P**H, as returned by ZGEBRD in its array
	  argument 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 illegal value