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    1:       SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            INFO, K, LDA, M, N
   10: *     ..
   11: *     .. Array Arguments ..
   12:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
   13: *     ..
   14: *
   15: *  Purpose
   16: *  =======
   17: *
   18: *  DORGR2 generates an m by n real matrix Q with orthonormal rows,
   19: *  which is defined as the last m rows of a product of k elementary
   20: *  reflectors of order n
   21: *
   22: *        Q  =  H(1) H(2) . . . H(k)
   23: *
   24: *  as returned by DGERQF.
   25: *
   26: *  Arguments
   27: *  =========
   28: *
   29: *  M       (input) INTEGER
   30: *          The number of rows of the matrix Q. M >= 0.
   31: *
   32: *  N       (input) INTEGER
   33: *          The number of columns of the matrix Q. N >= M.
   34: *
   35: *  K       (input) INTEGER
   36: *          The number of elementary reflectors whose product defines the
   37: *          matrix Q. M >= K >= 0.
   38: *
   39: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   40: *          On entry, the (m-k+i)-th row must contain the vector which
   41: *          defines the elementary reflector H(i), for i = 1,2,...,k, as
   42: *          returned by DGERQF in the last k rows of its array argument
   43: *          A.
   44: *          On exit, the m by n matrix Q.
   45: *
   46: *  LDA     (input) INTEGER
   47: *          The first dimension of the array A. LDA >= max(1,M).
   48: *
   49: *  TAU     (input) DOUBLE PRECISION array, dimension (K)
   50: *          TAU(i) must contain the scalar factor of the elementary
   51: *          reflector H(i), as returned by DGERQF.
   52: *
   53: *  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
   54: *
   55: *  INFO    (output) INTEGER
   56: *          = 0: successful exit
   57: *          < 0: if INFO = -i, the i-th argument has an illegal value
   58: *
   59: *  =====================================================================
   60: *
   61: *     .. Parameters ..
   62:       DOUBLE PRECISION   ONE, ZERO
   63:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   64: *     ..
   65: *     .. Local Scalars ..
   66:       INTEGER            I, II, J, L
   67: *     ..
   68: *     .. External Subroutines ..
   69:       EXTERNAL           DLARF, DSCAL, XERBLA
   70: *     ..
   71: *     .. Intrinsic Functions ..
   72:       INTRINSIC          MAX
   73: *     ..
   74: *     .. Executable Statements ..
   75: *
   76: *     Test the input arguments
   77: *
   78:       INFO = 0
   79:       IF( M.LT.0 ) THEN
   80:          INFO = -1
   81:       ELSE IF( N.LT.M ) THEN
   82:          INFO = -2
   83:       ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
   84:          INFO = -3
   85:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
   86:          INFO = -5
   87:       END IF
   88:       IF( INFO.NE.0 ) THEN
   89:          CALL XERBLA( 'DORGR2', -INFO )
   90:          RETURN
   91:       END IF
   92: *
   93: *     Quick return if possible
   94: *
   95:       IF( M.LE.0 )
   96:      $   RETURN
   97: *
   98:       IF( K.LT.M ) THEN
   99: *
  100: *        Initialise rows 1:m-k to rows of the unit matrix
  101: *
  102:          DO 20 J = 1, N
  103:             DO 10 L = 1, M - K
  104:                A( L, J ) = ZERO
  105:    10       CONTINUE
  106:             IF( J.GT.N-M .AND. J.LE.N-K )
  107:      $         A( M-N+J, J ) = ONE
  108:    20    CONTINUE
  109:       END IF
  110: *
  111:       DO 40 I = 1, K
  112:          II = M - K + I
  113: *
  114: *        Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
  115: *
  116:          A( II, N-M+II ) = ONE
  117:          CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
  118:      $               A, LDA, WORK )
  119:          CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
  120:          A( II, N-M+II ) = ONE - TAU( I )
  121: *
  122: *        Set A(m-k+i,n-k+i+1:n) to zero
  123: *
  124:          DO 30 L = N - M + II + 1, N
  125:             A( II, L ) = ZERO
  126:    30    CONTINUE
  127:    40 CONTINUE
  128:       RETURN
  129: *
  130: *     End of DORGR2
  131: *
  132:       END