DGELQ2 computes an LQ factorization of a real m-by-n matrix A:


    A = ( L 0 ) *  Q


 where:


    Q is a n-by-n orthogonal matrix;


    L is a lower-triangular m-by-m matrix;


    0 is a m-by-(n-m) zero matrix, if m < n.

M

          M is INTEGER


          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER


          The number of columns of the matrix A.  N >= 0.

A

          A is 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

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))


          The scalar factors of the elementary reflectors (see Further


          Details).

WORK

          WORK is DOUBLE PRECISION array, dimension (M)

INFO

          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

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  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**T


  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).