dormqr man page on Scientific

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DORMQR(1)		 LAPACK routine (version 3.2)		     DORMQR(1)

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

SYNOPSIS
       SUBROUTINE DORMQR( 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
       DORMQR 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 defined as the product of k elemen‐
       tary reflectors
	     Q = H(1) H(2) . . . H(k)
       as returned by DGEQRF. 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‐
	       QRF in the first 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 DGEQRF.

       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			     DORMQR(1)
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