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

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 sub-
	       array 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 trape-
	       zoidal matrix R; the remaining elements, with the array TAU, represent the orthog-
	       onal  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)


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