DORMBR(l)		LAPACK routine (version	1.1)		    DORMBR(l)

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

SYNOPSIS

  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(
		     LWORK )

PURPOSE
  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) respec-
  tively.

  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
	  K >= 0.  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.

  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) 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.

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