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DORMHR(1)		 LAPACK routine (version 3.2)		     DORMHR(1)

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

SYNOPSIS
       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(
			  * )

PURPOSE
       DORMHR overwrites the general real M-by-N matrix C with	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
       (MAX(1,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 per‐
	       formance 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 routine (version 3.2)	 November 2008			     DORMHR(1)
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