CXML
        	    
LAPACK version 3.0
dormbr(3)

PURPOSE
  DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
  with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNTAX
  SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
		     LWORK, INFO )

      CHARACTER	     SIDE, TRANS, VECT

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

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

DESCRIPTION
  If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with SIDE
  = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T':      Q**T * C
  C * Q**T

  If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C with
		  SIDE = 'L'	 SIDE = 'R'
  TRANS = 'N':	    P * C	   C * P
  TRANS = 'T':	    P**T * C	   C * P**T

  Here Q and P**T are the orthogonal matrices 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) and G(i)
  respectively.

  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of
  the orthogonal matrix Q or P**T that is applied.

  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k, Q =
  H(1) H(2) . . . H(k);
  if nq < k, Q = H(1) H(2) . . . H(nq-1).

  If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P =
  G(1) G(2) . . . G(k);
  if k >= nq, P = G(1) G(2) . . . G(nq-1).

ARGUMENTS
  VECT	  (input) CHARACTER*1
	  = 'Q': apply Q or Q**T;
	  = 'P': apply P or P**T.

  SIDE	  (input) CHARACTER*1
	  = 'L': apply Q, Q**T, P or P**T from the Left;
	  = 'R': apply Q, Q**T, P or P**T from the Right.

  TRANS	  (input) CHARACTER*1
	  = 'N':  No transpose, apply Q	 or P;
	  = 'T':  Transpose, apply Q**T or P**T.

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

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

  K	  (input) INTEGER
	  If VECT = 'Q', the number of columns in the original matrix reduced
	  by DGEBRD.  If VECT = 'P', the number of rows in the original
	  matrix reduced by DGEBRD.  K >= 0.

  A	  (input) DOUBLE PRECISION array, dimension
	  (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq)	if VECT = 'P' The
	  vectors which define the elementary reflectors H(i) and G(i), whose
	  products determine the matrices Q and P, as returned by DGEBRD.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 If VECT = 'Q', LDA >=
	  max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).

  TAU	  (input) DOUBLE PRECISION array, dimension (min(nq,K))
	  TAU(i) must contain the scalar factor of the elementary reflector
	  H(i) or G(i) which determines Q or P, as returned by DGEBRD in the
	  array argument TAUQ or TAUP.

  C	  (input/output) DOUBLE PRECISION array, dimension (LDC,N)
	  On entry, the M-by-N matrix C.  On exit, C is overwritten by Q*C or
	  Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.

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

  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.  If SIDE = 'L', LWORK >= max(1,N);
	  if SIDE = 'R', LWORK >= max(1,M).  For optimum performance LWORK >=
	  N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', 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