CXML
        	    
LAPACK version 3.0
dormhr(3)

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

SYNTAX
  SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK,
		     LWORK, INFO )

      CHARACTER	     SIDE, TRANS

      INTEGER	     IHI, ILO, INFO, LDA, LDC, LWORK, M, N

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

DESCRIPTION
  DORMHR 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 of order nq, with nq = m if SIDE = 'L'
  and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO elementary
  reflectors, as returned by DGEHRD:

  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

  ILO	  (input) INTEGER
	  IHI	  (input) INTEGER ILO and IHI must have the same values as in
	  the previous call of DGEHRD. Q is equal to the unit matrix except
	  in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE = 'L', then 1 <=
	  ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if
	  SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and
	  IHI = 0, if N = 0.

  A	  (input) DOUBLE PRECISION array, dimension
	  (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
	  define the elementary reflectors, as returned by DGEHRD.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,M) if SIDE =
	  'L'; LDA >= max(1,N) if SIDE = 'R'.

  TAU	  (input) DOUBLE PRECISION array, dimension
	  (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
	  scalar factor of the elementary reflector H(i), as returned by
	  DGEHRD.

  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.

  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