CXML
        	    
LAPACK version 3.0
dorgbr(3)

PURPOSE
  DORGBR - generate one of the real orthogonal matrices Q or P**T determined
  by DGEBRD when reducing a real matrix A to bidiagonal form

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

      CHARACTER	     VECT

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

      DOUBLE	     PRECISION A( LDA, * ), TAU( * ), WORK( * )

DESCRIPTION
  DORGBR generates one of the real orthogonal matrices Q or P**T determined
  by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B *
  P**T. Q and P**T 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 DORGBR returns the first n columns
  of Q, where m >= n >= k;
  if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M
  matrix.

  If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of
  order N:
  if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m rows
  of P**T, where n >= m >= k;
  if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an N-
  by-N matrix.

ARGUMENTS
  VECT	  (input) CHARACTER*1
	  Specifies whether the matrix Q or the matrix P**T is required, as
	  defined in the transformation applied by DGEBRD:
	  = 'Q':  generate Q;
	  = 'P':  generate P**T.

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

  N	  (input) INTEGER
	  The number of columns of the matrix Q or P**T 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 DGEBRD.  If VECT = 'P', the number of rows in the
	  original K-by-N matrix reduced by DGEBRD.  K >= 0.

  A	  (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	  On entry, the vectors which define the elementary reflectors, as
	  returned by DGEBRD.  On exit, the M-by-N matrix Q or P**T.

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

  TAU	  (input) DOUBLE PRECISION 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**T, as returned by DGEBRD in its array
	  argument TAUQ or TAUP.

  WORK	  (workspace/output) DOUBLE PRECISION 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