      SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, L, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DORMRZ overwrites the general real M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'T':      Q**T * C       C * Q**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**T from the Left;
*          = 'R': apply Q or Q**T from the Right.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'T':  Transpose, apply Q**T.
*
*  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**H*C or C*Q**H or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If SIDE = 'L', LWORK >= max(1,N);
*          if SIDE = 'R', LWORK >= max(1,M).
*          For optimum performance LWORK >= N*NB if SIDE = 'L', and
*          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
*          blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  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
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            NBMAX, LDT
      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY, NOTRAN
      CHARACTER          TRANST
      INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC,
     $                   LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   T( LDT, NBMAX )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLARZB, DLARZT, DORMR3, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      LEFT = LSAME( SIDE, 'L' )
      NOTRAN = LSAME( TRANS, 'N' )
      LQUERY = ( LWORK.EQ.-1 )
*
*     NQ is the order of Q and NW is the minimum dimension of WORK
*
      IF( LEFT ) THEN
         NQ = M
         NW = N
      ELSE
         NQ = N
         NW = M
      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
      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
         INFO = -13
      END IF
*
      IF( INFO.EQ.0 ) THEN
*
*        Determine the block size.  NB may be at most NBMAX, where NBMAX
*        is used to define the local array T.
*
         NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N, K,
     $        -1 ) )
         LWKOPT = MAX( 1, NW )*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DORMRZ', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      LDWORK = NW
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
         IWS = NW*NB
         IF( LWORK.LT.IWS ) THEN
            NB = LWORK / LDWORK
            NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K,
     $              -1 ) )
         END IF
      ELSE
         IWS = NW
      END IF
*
      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
*
*        Use unblocked code
*
         CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
     $                WORK, IINFO )
      ELSE
*
*        Use blocked code
*
         IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
     $       ( .NOT.LEFT .AND. NOTRAN ) ) THEN
            I1 = 1
            I2 = K
            I3 = NB
         ELSE
            I1 = ( ( K-1 ) / NB )*NB + 1
            I2 = 1
            I3 = -NB
         END IF
*
         IF( LEFT ) THEN
            NI = N
            JC = 1
            JA = M - L + 1
         ELSE
            MI = M
            IC = 1
            JA = N - L + 1
         END IF
*
         IF( NOTRAN ) THEN
            TRANST = 'T'
         ELSE
            TRANST = 'N'
         END IF
*
         DO 10 I = I1, I2, I3
            IB = MIN( NB, K-I+1 )
*
*           Form the triangular factor of the block reflector
*           H = H(i+ib-1) . . . H(i+1) H(i)
*
            CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
     $                   TAU( I ), T, LDT )
*
            IF( LEFT ) THEN
*
*              H or H' is applied to C(i:m,1:n)
*
               MI = M - I + 1
               IC = I
            ELSE
*
*              H or H' is applied to C(1:m,i:n)
*
               NI = N - I + 1
               JC = I
            END IF
*
*           Apply H or H'
*
            CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
     $                   IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
     $                   LDC, WORK, LDWORK )
   10    CONTINUE
*
      END IF
*
      WORK( 1 ) = LWKOPT
*
      RETURN
*
*     End of DORMRZ
*
      END
