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      SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
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*
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*  -- LAPACK routine (version 3.2.2) --
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*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
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*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*     June 2010
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*
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*     .. Scalar Arguments ..
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      INTEGER            INFO, LDA, M, N
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*     ..
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*     .. Array Arguments ..
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      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  DGEQR2 computes a QR factorization of a real m by n matrix A:
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*  A = Q * R.
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*
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*  Arguments
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*  =========
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*
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*  M       (input) INTEGER
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*          The number of rows of the matrix A.  M >= 0.
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*
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*  N       (input) INTEGER
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*          The number of columns of the matrix A.  N >= 0.
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*
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*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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*          On entry, the m by n matrix A.
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*          On exit, the elements on and above the diagonal of the array
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*          contain the min(m,n) by n upper trapezoidal matrix R (R is
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*          upper triangular if m >= n); the elements below the diagonal,
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*          with the array TAU, represent the orthogonal matrix Q as a
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*          product of elementary reflectors (see Further Details).
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*
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*  LDA     (input) INTEGER
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*          The leading dimension of the array A.  LDA >= max(1,M).
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*
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*  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
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*          The scalar factors of the elementary reflectors (see Further
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*          Details).
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*
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*  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
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*
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*  INFO    (output) INTEGER
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*          = 0: successful exit
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*          < 0: if INFO = -i, the i-th argument had an illegal value
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*
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*  Further Details
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*  ===============
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*
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*  The matrix Q is represented as a product of elementary reflectors
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*
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*     Q = H(1) H(2) . . . H(k), where k = min(m,n).
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*
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*  Each H(i) has the form
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*
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*     H(i) = I - tau * v * v'
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*
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*  where tau is a real scalar, and v is a real vector with
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*  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
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*  and tau in TAU(i).
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*
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*  =====================================================================
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*
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*     .. Parameters ..
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      DOUBLE PRECISION   ONE
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      PARAMETER          ( ONE = 1.0D+0 )
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*     ..
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*     .. Local Scalars ..
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      INTEGER            I, K
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      DOUBLE PRECISION   AII
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*     ..
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*     .. External Subroutines ..
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      EXTERNAL           DLARF, DLARFG, XERBLA
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*     ..
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*     .. Intrinsic Functions ..
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      INTRINSIC          MAX, MIN
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input arguments
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*
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      INFO = 0
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      IF( M.LT.0 ) THEN
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         INFO = -1
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      ELSE IF( N.LT.0 ) THEN
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         INFO = -2
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      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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         INFO = -4
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      END IF
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      IF( INFO.NE.0 ) THEN
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         CALL XERBLA( 'DGEQR2', -INFO )
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         RETURN
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      END IF
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*
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      K = MIN( M, N )
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*
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      DO 10 I = 1, K
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*
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*        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
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*
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         CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
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     $                TAU( I ) )
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         IF( I.LT.N ) THEN
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*
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*           Apply H(i) to A(i:m,i+1:n) from the left
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*
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            AII = A( I, I )
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            A( I, I ) = ONE
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            CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
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     $                  A( I, I+1 ), LDA, WORK )
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            A( I, I ) = AII
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         END IF
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   10 CONTINUE
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      RETURN
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*
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*     End of DGEQR2
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*
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      END