sgeqrf(l) [redhat man page]

SGEQRF(l)								 )								 SGEQRF(l)

NAME

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

SYNOPSIS

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

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE

       SGEQRF 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) REAL 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 trape-
	       zoidal 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) 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,N).  For optimum performance LWORK >= N*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(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).

LAPACK version 3.0						   15 June 2000 							 SGEQRF(l)