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DGEQLF(1)		 LAPACK routine (version 3.2)		     DGEQLF(1)

NAME
       DGEQLF - computes 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  subarray  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 trapezoidal
	       matrix L; the remaining elements, with the array TAU, represent
	       the  orthogonal	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
       (MAX(1,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 opti‐
	       mum performance LWORK >= N*NB, where NB is the  optimal	block‐
	       size.   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 routine (version 3.2)	 November 2008			     DGEQLF(1)
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