          SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DGEQR2 computes a QR factorization of a real m by n matrix A:
    *  A = Q * R.
    *
    *  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 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     (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(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i),
    *  and tau in TAU(i).
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE
          PARAMETER          ( ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, K
          DOUBLE PRECISION   AII
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLARF, DLARFG, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -4
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DGEQR2', -INFO )
             RETURN
          END IF
    *
          K = MIN( M, N )
    *
          DO 10 I = 1, K
    *
    *        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
    *
             CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
         $                TAU( I ) )
             IF( I.LT.N ) THEN
    *
    *           Apply H(i) to A(i:m,i+1:n) from the left
    *
                AII = A( I, I )
                A( I, I ) = ONE
                CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
         $                  A( I, I+1 ), LDA, WORK )
                A( I, I ) = AII
             END IF
       10 CONTINUE
          RETURN
    *
    *     End of DGEQR2
    *
          END