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RedHat 9 (Linux i386) - man page for sgeqrf (redhat section l)

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 trapezoidal matrix R (R is upper  trian-
	       gular  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  Fur-
	       ther 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)


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