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      SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,

     $                   WORK, INFO )

*

*  -- LAPACK routine (version 3.2) --

*  -- LAPACK is a software package provided by Univ. of Tennessee,    --

*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--

*     November 2006

*

*     .. Scalar Arguments ..

      CHARACTER          SIDE, TRANS

      INTEGER            INFO, K, L, LDA, LDC, M, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

*     ..

*

*  Purpose

*  =======

*

*  DORMR3 overwrites the general real m by n matrix C with

*

*        Q * C  if SIDE = 'L' and TRANS = 'N', or

*

*        Q'* C  if SIDE = 'L' and TRANS = 'T', or

*

*        C * Q  if SIDE = 'R' and TRANS = 'N', or

*

*        C * Q' if SIDE = 'R' and TRANS = 'T',

*

*  where Q is a real orthogonal matrix defined as the product of k

*  elementary reflectors

*

*        Q = H(1) H(2) . . . H(k)

*

*  as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n

*  if SIDE = 'R'.

*

*  Arguments

*  =========

*

*  SIDE    (input) CHARACTER*1

*          = 'L': apply Q or Q' from the Left

*          = 'R': apply Q or Q' from the Right

*

*  TRANS   (input) CHARACTER*1

*          = 'N': apply Q  (No transpose)

*          = 'T': apply Q' (Transpose)

*

*  M       (input) INTEGER

*          The number of rows of the matrix C. M >= 0.

*

*  N       (input) INTEGER

*          The number of columns of the matrix C. N >= 0.

*

*  K       (input) INTEGER

*          The number of elementary reflectors whose product defines

*          the matrix Q.

*          If SIDE = 'L', M >= K >= 0;

*          if SIDE = 'R', N >= K >= 0.

*

*  L       (input) INTEGER

*          The number of columns of the matrix A containing

*          the meaningful part of the Householder reflectors.

*          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.

*

*  A       (input) DOUBLE PRECISION array, dimension

*                               (LDA,M) if SIDE = 'L',

*                               (LDA,N) if SIDE = 'R'

*          The i-th row must contain the vector which defines the

*          elementary reflector H(i), for i = 1,2,...,k, as returned by

*          DTZRZF in the last k rows of its array argument A.

*          A is modified by the routine but restored on exit.

*

*  LDA     (input) INTEGER

*          The leading dimension of the array A. LDA >= max(1,K).

*

*  TAU     (input) DOUBLE PRECISION array, dimension (K)

*          TAU(i) must contain the scalar factor of the elementary

*          reflector H(i), as returned by DTZRZF.

*

*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)

*          On entry, the m-by-n matrix C.

*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.

*

*  LDC     (input) INTEGER

*          The leading dimension of the array C. LDC >= max(1,M).

*

*  WORK    (workspace) DOUBLE PRECISION array, dimension

*                                   (N) if SIDE = 'L',

*                                   (M) if SIDE = 'R'

*

*  INFO    (output) INTEGER

*          = 0: successful exit

*          < 0: if INFO = -i, the i-th argument had an illegal value

*

*  Further Details

*  ===============

*

*  Based on contributions by

*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

*

*  =====================================================================

*

*     .. Local Scalars ..

      LOGICAL            LEFT, NOTRAN

      INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     ..

*     .. External Subroutines ..

      EXTERNAL           DLARZ, XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX

*     ..

*     .. Executable Statements ..

*

*     Test the input arguments

*

      INFO = 0

      LEFT = LSAME( SIDE, 'L' )

      NOTRAN = LSAME( TRANS, 'N' )

*

*     NQ is the order of Q

*

      IF( LEFT ) THEN

         NQ = M

      ELSE

         NQ = N

      END IF

      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN

         INFO = -1

      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN

         INFO = -2

      ELSE IF( M.LT.0 ) THEN

         INFO = -3

      ELSE IF( N.LT.0 ) THEN

         INFO = -4

      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN

         INFO = -5

      ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.

     $         ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN

         INFO = -6

      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN

         INFO = -8

      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN

         INFO = -11

      END IF

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'DORMR3', -INFO )

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )

     $   RETURN

*

      IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN

         I1 = 1

         I2 = K

         I3 = 1

      ELSE

         I1 = K

         I2 = 1

         I3 = -1

      END IF

*

      IF( LEFT ) THEN

         NI = N

         JA = M - L + 1

         JC = 1

      ELSE

         MI = M

         JA = N - L + 1

         IC = 1

      END IF

*

      DO 10 I = I1, I2, I3

         IF( LEFT ) THEN

*

*           H(i) or H(i)' is applied to C(i:m,1:n)

*

            MI = M - I + 1

            IC = I

         ELSE

*

*           H(i) or H(i)' is applied to C(1:m,i:n)

*

            NI = N - I + 1

            JC = I

         END IF

*

*        Apply H(i) or H(i)'

*

         CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),

     $               C( IC, JC ), LDC, WORK )

*

   10 CONTINUE

*

      RETURN

*

*     End of DORMR3

*

      END