SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, &
                         T, LDT, C, LDC, WORK, LDWORK )
!
!  -- LAPACK auxiliary routine (version 3.1) --
!     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
!     November 2006
!
!     .. Scalar Arguments ..
      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
!     ..
!     .. Array Arguments ..
      DOUBLE PRECISION   C( LDC, * ), T( LDT, * ), V( LDV, * ), &
                         WORK( LDWORK, * )
!     ..
!
!  Purpose
!  =======
!
!  DLARFB applies a real block reflector H or its transpose H' to a
!  real m by n matrix C, from either the left or the right.
!
!  Arguments
!  =========
!
!  SIDE    (input) CHARACTER*1
!          = 'L': apply H or H' from the Left
!          = 'R': apply H or H' from the Right
!
!  TRANS   (input) CHARACTER*1
!          = 'N': apply H (No transpose)
!          = 'T': apply H' (Transpose)
!
!  DIRECT  (input) CHARACTER*1
!          Indicates how H is formed from a product of elementary
!          reflectors
!          = 'F': H = H(1) H(2) . . . H(k) (Forward)
!          = 'B': H = H(k) . . . H(2) H(1) (Backward)
!
!  STOREV  (input) CHARACTER*1
!          Indicates how the vectors which define the elementary
!          reflectors are stored:
!          = 'C': Columnwise
!          = 'R': Rowwise
!
!  M       (input) INTEGER
!          The number of rows of the matrix C.
!
!  N       (input) INTEGER
!          The number of columns of the matrix C.
!
!  K       (input) INTEGER
!          The order of the matrix T (= the number of elementary
!          reflectors whose product defines the block reflector).
!
!  V       (input) DOUBLE PRECISION array, dimension
!                                (LDV,K) if STOREV = 'C'
!                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
!                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
!          The matrix V. See further details.
!
!  LDV     (input) INTEGER
!          The leading dimension of the array V.
!          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
!          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
!          if STOREV = 'R', LDV >= K.
!
!  T       (input) DOUBLE PRECISION array, dimension (LDT,K)
!          The triangular k by k matrix T in the representation of the
!          block reflector.
!
!  LDT     (input) INTEGER
!          The leading dimension of the array T. LDT >= K.
!
!  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
!          On entry, the m by n matrix C.
!          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
!
!  LDC     (input) INTEGER
!          The leading dimension of the array C. LDA >= max(1,M).
!
!  WORK    (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
!
!  LDWORK  (input) INTEGER
!          The leading dimension of the array WORK.
!          If SIDE = 'L', LDWORK >= max(1,N);
!          if SIDE = 'R', LDWORK >= max(1,M).
!
!  =====================================================================
!
!     .. Parameters ..
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
!     ..
!     .. Local Scalars ..
      CHARACTER          TRANST
      INTEGER            I, J
!     ..
!     .. External Functions ..
!     LOGICAL            LSAME
!     EXTERNAL           LSAME
!     ..
!     .. External Subroutines ..
!     EXTERNAL           DCOPY, DGEMM, DTRMM
!     ..
!     .. Executable Statements ..
!
!     Quick return if possible
!
      IF( M.LE.0 .OR. N.LE.0 ) &
         RETURN
!
      IF( LSAME( TRANS, 'N' ) ) THEN
         TRANST = 'T'
      ELSE
         TRANST = 'N'
      END IF
!
      IF( LSAME( STOREV, 'C' ) ) THEN
!
         IF( LSAME( DIRECT, 'F' ) ) THEN
!
!           Let  V =  ( V1 )    (first K rows)
!                     ( V2 )
!           where  V1  is unit lower triangular.
!
            IF( LSAME( SIDE, 'L' ) ) THEN
!
!              Form  H * C  or  H' * C  where  C = ( C1 )
!                                                  ( C2 )
!
!              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
!
!              W := C1'
!
               DO 10 J = 1, K
                  CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
   10          CONTINUE
!
!              W := W * V1
!
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, &
                           K, ONE, V, LDV, WORK, LDWORK )
               IF( M.GT.K ) THEN
!
!                 W := W + C2'*V2
!
                  CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, &
                              ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, &
                              ONE, WORK, LDWORK )
               END IF
!
!              W := W * T'  or  W * T
!
               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - V * W'
!
               IF( M.GT.K ) THEN
!
!                 C2 := C2 - V2 * W'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, &
                              -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, &
                              C( K+1, 1 ), LDC )
               END IF
!
!              W := W * V1'
!
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, &
                           ONE, V, LDV, WORK, LDWORK )
!
!              C1 := C1 - W'
!
               DO 30 J = 1, K
                  DO 20 I = 1, N
                     C( J, I ) = C( J, I ) - WORK( I, J )
   20             CONTINUE
   30          CONTINUE
!
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
!
!              Form  C * H  or  C * H'  where  C = ( C1  C2 )
!
!              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
!
!              W := C1
!
               DO 40 J = 1, K
                  CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
   40          CONTINUE
!
!              W := W * V1
!
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, &
                           K, ONE, V, LDV, WORK, LDWORK )
               IF( N.GT.K ) THEN
!
!                 W := W + C2 * V2
!
                  CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, &
                              ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, &
                              ONE, WORK, LDWORK )
               END IF
!
!              W := W * T  or  W * T'
!
               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - W * V'
!
               IF( N.GT.K ) THEN
!
!                 C2 := C2 - W * V2'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, &
                              -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, &
                              C( 1, K+1 ), LDC )
               END IF
!
!              W := W * V1'
!
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, &
                           ONE, V, LDV, WORK, LDWORK )
!
!              C1 := C1 - W
!
               DO 60 J = 1, K
                  DO 50 I = 1, M
                     C( I, J ) = C( I, J ) - WORK( I, J )
   50             CONTINUE
   60          CONTINUE
            END IF
!
         ELSE
!
!           Let  V =  ( V1 )
!                     ( V2 )    (last K rows)
!           where  V2  is unit upper triangular.
!
            IF( LSAME( SIDE, 'L' ) ) THEN
!
!              Form  H * C  or  H' * C  where  C = ( C1 )
!                                                  ( C2 )
!
!              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
!
!              W := C2'
!
               DO 70 J = 1, K
                  CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
   70          CONTINUE
!
!              W := W * V2
!
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, &
                           K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
               IF( M.GT.K ) THEN
!
!                 W := W + C1'*V1
!
                  CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, &
                              ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
!
!              W := W * T'  or  W * T
!
               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - V * W'
!
               IF( M.GT.K ) THEN
!
!                 C1 := C1 - V1 * W'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, &
                              -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
               END IF
!
!              W := W * V2'
!
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, &
                           ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
!
!              C2 := C2 - W'
!
               DO 90 J = 1, K
                  DO 80 I = 1, N
                     C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J )
   80             CONTINUE
   90          CONTINUE
!
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
!
!              Form  C * H  or  C * H'  where  C = ( C1  C2 )
!
!              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
!
!              W := C2
!
               DO 100 J = 1, K
                  CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
  100          CONTINUE
!
!              W := W * V2
!
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, &
                           K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
               IF( N.GT.K ) THEN
!
!                 W := W + C1 * V1
!
                  CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, &
                              ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
!
!              W := W * T  or  W * T'
!
               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - W * V'
!
               IF( N.GT.K ) THEN
!
!                 C1 := C1 - W * V1'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, &
                              -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
               END IF
!
!              W := W * V2'
!
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, &
                           ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
!
!              C2 := C2 - W
!
               DO 120 J = 1, K
                  DO 110 I = 1, M
                     C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
  110             CONTINUE
  120          CONTINUE
            END IF
         END IF
!
      ELSE IF( LSAME( STOREV, 'R' ) ) THEN
!
         IF( LSAME( DIRECT, 'F' ) ) THEN
!
!           Let  V =  ( V1  V2 )    (V1: first K columns)
!           where  V1  is unit upper triangular.
!
            IF( LSAME( SIDE, 'L' ) ) THEN
!
!              Form  H * C  or  H' * C  where  C = ( C1 )
!                                                  ( C2 )
!
!              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
!
!              W := C1'
!
               DO 130 J = 1, K
                  CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
  130          CONTINUE
!
!              W := W * V1'
!
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, &
                           ONE, V, LDV, WORK, LDWORK )
               IF( M.GT.K ) THEN
!
!                 W := W + C2'*V2'
!
                  CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, &
                              C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, &
                              WORK, LDWORK )
               END IF
!
!              W := W * T'  or  W * T
!
               CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - V' * W'
!
               IF( M.GT.K ) THEN
!
!                 C2 := C2 - V2' * W'
!
                  CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, &
                              V( 1, K+1 ), LDV, WORK, LDWORK, ONE, &
                              C( K+1, 1 ), LDC )
               END IF
!
!              W := W * V1
!
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, &
                           K, ONE, V, LDV, WORK, LDWORK )
!
!              C1 := C1 - W'
!
               DO 150 J = 1, K
                  DO 140 I = 1, N
                     C( J, I ) = C( J, I ) - WORK( I, J )
  140             CONTINUE
  150          CONTINUE
!
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
!
!              Form  C * H  or  C * H'  where  C = ( C1  C2 )
!
!              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
!
!              W := C1
!
               DO 160 J = 1, K
                  CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
  160          CONTINUE
!
!              W := W * V1'
!
               CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, &
                           ONE, V, LDV, WORK, LDWORK )
               IF( N.GT.K ) THEN
!
!                 W := W + C2 * V2'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, &
                              ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, &
                              ONE, WORK, LDWORK )
               END IF
!
!              W := W * T  or  W * T'
!
               CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - W * V
!
               IF( N.GT.K ) THEN
!
!                 C2 := C2 - W * V2
!
                  CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, &
                              -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, &
                              C( 1, K+1 ), LDC )
               END IF
!
!              W := W * V1
!
               CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, &
                           K, ONE, V, LDV, WORK, LDWORK )
!
!              C1 := C1 - W
!
               DO 180 J = 1, K
                  DO 170 I = 1, M
                     C( I, J ) = C( I, J ) - WORK( I, J )
  170             CONTINUE
  180          CONTINUE
!
            END IF
!
         ELSE
!
!           Let  V =  ( V1  V2 )    (V2: last K columns)
!           where  V2  is unit lower triangular.
!
            IF( LSAME( SIDE, 'L' ) ) THEN
!
!              Form  H * C  or  H' * C  where  C = ( C1 )
!                                                  ( C2 )
!
!              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
!
!              W := C2'
!
               DO 190 J = 1, K
                  CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
  190          CONTINUE
!
!              W := W * V2'
!
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, &
                           ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
               IF( M.GT.K ) THEN
!
!                 W := W + C1'*V1'
!
                  CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, &
                              C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
!
!              W := W * T'  or  W * T
!
               CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - V' * W'
!
               IF( M.GT.K ) THEN
!
!                 C1 := C1 - V1' * W'
!
                  CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, &
                              V, LDV, WORK, LDWORK, ONE, C, LDC )
               END IF
!
!              W := W * V2
!
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, &
                           K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
!
!              C2 := C2 - W'
!
               DO 210 J = 1, K
                  DO 200 I = 1, N
                     C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J )
  200             CONTINUE
  210          CONTINUE
!
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
!
!              Form  C * H  or  C * H'  where  C = ( C1  C2 )
!
!              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
!
!              W := C2
!
               DO 220 J = 1, K
                  CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
  220          CONTINUE
!
!              W := W * V2'
!
               CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, &
                           ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
               IF( N.GT.K ) THEN
!
!                 W := W + C1 * V1'
!
                  CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, &
                              ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
!
!              W := W * T  or  W * T'
!
               CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, &
                           ONE, T, LDT, WORK, LDWORK )
!
!              C := C - W * V
!
               IF( N.GT.K ) THEN
!
!                 C1 := C1 - W * V1
!
                  CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, &
                              -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
               END IF
!
!              W := W * V2
!
               CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, &
                           K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
!
!              C1 := C1 - W
!
               DO 240 J = 1, K
                  DO 230 I = 1, M
                     C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
  230             CONTINUE
  240          CONTINUE
!
            END IF
!
         END IF
      END IF
!
      RETURN
!
!     End of DLARFB
!
      END SUBROUTINE DLARFB