CXML
        	    
LAPACK version 3.0
sormrq(3)

PURPOSE
  SORMRQ - overwrite the general real M-by-N matrix C with  SIDE = 'L' SIDE =
  'R' TRANS = 'N'

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

      CHARACTER	     SIDE, TRANS

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

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

DESCRIPTION
  SORMRQ 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

  where Q is a real orthogonal matrix defined as the product of k elementary
  reflectors

	Q = H(1) H(2) . . . H(k)

  as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N if SIDE
  = 'R'.

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

  TRANS	  (input) CHARACTER*1
	  = 'N':  No transpose, apply Q;
	  = 'T':  Transpose, apply Q**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
	  The number of elementary reflectors whose product defines the
	  matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

  A	  (input) REAL array, dimension
	  (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
	  contain the vector which defines the elementary reflector H(i), for
	  i = 1,2,...,k, as returned by SGERQF in the last k rows of its
	  array argument A.  A is modified by the routine but restored on
	  exit.

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

  TAU	  (input) REAL array, dimension (K)
	  TAU(i) must contain the scalar factor of the elementary reflector
	  H(i), as returned by SGERQF.

  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.

  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