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DORMQL(l)			       )			     DORMQL(l)

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

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

	   CHARACTER	  SIDE, TRANS

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

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

PURPOSE
       DORMQL 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 elemen‐
       tary reflectors

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

       as  returned by DGEQLF. 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) DOUBLE PRECISION array, dimension (LDA,K)
	       The i-th column must contain the vector which defines the  ele‐
	       mentary	reflector H(i), for i = 1,2,...,k, as returned by DGE‐
	       QLF in the last k columns of its array argument A.  A is	 modi‐
	       fied by the routine but restored on exit.

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

       TAU     (input) DOUBLE PRECISION array, dimension (K)
	       TAU(i) must contain the scalar factor of the elementary reflec‐
	       tor H(i), as returned by DGEQLF.

       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 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 version 3.0		 15 June 2000			     DORMQL(l)
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