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LAPACK version 3.0
dgeql2(3)

PURPOSE
  DGEQL2 - compute a QL factorization of a real m by n matrix A

SYNTAX
  SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )

      INTEGER	     INFO, LDA, M, N

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

DESCRIPTION
  DGEQL2 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) DOUBLE PRECISION array, dimension (N)

  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).