SGERQF(l)		LAPACK routine (version	1.1)		    SGERQF(l)

NAME
  SGERQF - compute an RQ factorization of a real M-by-N	matrix A

SYNOPSIS

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

      INTEGER	     INFO, LDA,	LWORK, M, N

      REAL	     A(	LDA, * ), TAU( * ), WORK( LWORK	)

PURPOSE
  SGERQF computes an RQ	factorization of a real	M-by-N matrix A: A = R * Q.

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) REAL array, dimension (LDA,N)
	  On entry, the	M-by-N matrix A.  On exit, if m	<= n, the upper	tri-
	  angle	of the subarray	A(1:m,n-m+1:n) contains	the M-by-M upper tri-
	  angular matrix R; if m >= n, the elements on and above the (m-n)-th
	  subdiagonal contain the M-by-N upper trapezoidal matrix R; the
	  remaining elements, 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) REAL	array, dimension (min(M,N))
	  The scalar factors of	the elementary reflectors (see Further
	  Details).

  WORK	  (workspace) REAL 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,M).	For optimum
	  performance LWORK >= M*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(n-k+i+1:n) = 0 and v(n-k+i)	= 1; v(1:n-k+i-1) is stored on exit in A(m-
  k+i,1:n-k+i-1), and tau in TAU(i).