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SORMBR(l)					)					SORMBR(l)

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

SYNOPSIS
       SUBROUTINE SORMBR( 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

	   REAL 	  A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE
       If VECT = 'Q', SORMBR 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', SORMBR 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 SGEBRD when reducing a real
       matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T are defined as products of  ele-
       mentary 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 SGEBRD.  If
	       VECT = 'P', the number of rows in the original matrix reduced by SGEBRD.  K >= 0.

       A       (input) REAL 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 SGEBRD.

       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) REAL 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 SGEBRD in the array argument TAUQ or TAUP.

       C       (input/output) REAL 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) REAL 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

LAPACK version 3.0			   15 June 2000 				SORMBR(l)
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