DGEQR2 computes a QR factorization of a real m by n matrix A:
 A = Q * R.

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

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

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the m by n matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(m,n) by n upper trapezoidal matrix R (R is
          upper triangular if m >= n); the elements below the diagonal,
          with the array TAU, represent the orthogonal matrix Q as a
          product of elementary reflectors (see Further Details).

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

          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

          WORK is DOUBLE PRECISION array, dimension (N)

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

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i),
  and tau in TAU(i).