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LAPACK version 3.0
dgelq2(3)

PURPOSE
  DGELQ2 - compute an LQ factorization of a real m by n matrix A

SYNTAX
  SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )

      INTEGER	     INFO, LDA, M, N

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

DESCRIPTION
  DGELQ2 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) DOUBLE PRECISION array, dimension (M)

  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).