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DGEQLF(l)					)					DGEQLF(l)

NAME
       DGEQLF - compute a QL factorization of a real M-by-N matrix A

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

	   INTEGER	  INFO, LDA, LWORK, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L.

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) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, if m >= n, the lower triangle of the sub-
	       array A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the
	       elements  on  and below the (n-m)-th superdiagonal contain the M-by-N lower trape-
	       zoidal matrix L; the remaining elements, with the array TAU, represent the orthog-
	       onal  matrix  Q	as a product of elementary reflectors (see Further Details).  LDA
	       (input) INTEGER The leading dimension of the array A.  LDA >= max(1,M).

       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace/output) DOUBLE PRECISION 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(k) . . . H(2) H(1), 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(m-k+i+1:m)  =	0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i),
       and tau in TAU(i).

LAPACK version 3.0			   15 June 2000 				DGEQLF(l)
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