redhat man page for sgerqf

SGERQF(l)								 )								 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( * )

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 triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
	       triangular 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/output) 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.

	       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

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).

LAPACK version 3.0						   15 June 2000 							 SGERQF(l)