text:       SUBROUTINE SGEQR2( M, N, A, LDA, TAU, WORK, INFO )
  *
  *  -- LAPACK routine (version 3.0) --
  *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
  *     Courant Institute, Argonne National Lab, and Rice University
  *     February 29, 1992
  *
  *     .. Scalar Arguments ..
        INTEGER            INFO, LDA, M, N
  *     ..
  *     .. Array Arguments ..
        REAL               A( LDA, * ), TAU( * ), WORK( * )
  *     ..
  *
  *  Purpose
  *  =======
  *
  *  SGEQR2 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) REAL 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) REAL array, dimension (min(M,N))
  *          The scalar factors of the elementary reflectors (see Further
  *          Details).
  *
  *  WORK    (workspace) REAL 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 ..
        REAL               ONE
        PARAMETER          ( ONE = 1.0E+0 )
  *     ..
  *     .. Local Scalars ..
        INTEGER            I, K
        REAL               AII
  *     ..
  *     .. External Subroutines ..
        EXTERNAL           SLARF, SLARFG, 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( 'SGEQR2', -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 SLARFG( 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 SLARF( '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 SGEQR2
  *
        END
  