DGEQRF(l)		LAPACK routine (version	1.1)		    DGEQRF(l)

NAME
  DGEQRF - compute a QR	factorization of a real	M-by-N matrix A

SYNOPSIS

  SUBROUTINE DGEQRF( M,	N, A, LDA, TAU,	WORK, LWORK, INFO )

      INTEGER	     INFO, LDA,	LWORK, M, N

      DOUBLE	     PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE
  DGEQRF computes a QR factorization of	a real M-by-N matrix A:	A = Q *	R.

ARGUMENTS

  M	  (input) INTEGER
	  The number of	rows of	the matrix A.  M >= 0.

  N	  (input) INTEGER
	  The number of	columns	of the matrix A.  N >= 0.

  A	  (input/output) DOUBLE	PRECISION array, dimension (LDA,N)
	  On entry, the	M-by-N matrix A.  On exit, the elements	on and above
	  the diagonal of the array contain the	min(M,N)-by-N upper tra-
	  pezoidal matrix R (R is upper	triangular if m	>= n); the elements
	  below	the diagonal, with the array TAU, represent the	orthogonal
	  matrix Q as a	product	of min(m,n) elementary reflectors (see
	  Further Details).

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

  TAU	  (output) DOUBLE PRECISION array, dimension (min(M,N))
	  The scalar factors of	the elementary reflectors (see Further
	  Details).

  WORK	  (workspace) 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.  LWORK >= max(1,N).	For optimum
	  performance LWORK >= N*NB, where NB is the optimal blocksize.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO	= -i, the i-th argument	had an illegal value

FURTHER	DETAILS
  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has	the form

     H(i) = I -	tau * v	* v'

  where	tau is a real scalar, and v is a real vector with
  v(1:i-1) = 0 and v(i)	= 1; v(i+1:m) is stored	on exit	in A(i+1:m,i), and
  tau in TAU(i).