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LAPACK version 3.0
dgelqf(3)

PURPOSE
  DGELQF - compute an LQ factorization of a real M-by-N matrix A

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

      INTEGER	     INFO, LDA, LWORK, M, N

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

DESCRIPTION
  DGELQF computes an LQ factorization of a real M-by-N matrix A: A = L * 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) DOUBLE PRECISION array, dimension (LDA,N)
	  On entry, the M-by-N matrix A.  On exit, the elements on and below
	  the diagonal of the array contain the m-by-min(m,n) lower
	  trapezoidal matrix L (L is lower triangular if m <= n); the
	  elements above the diagonal, 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 (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(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(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and
  tau in TAU(i).