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      SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
     $                   T, LDT, C, LDC, WORK, LDWORK )
      IMPLICIT NONE
*
*  -- LAPACK auxiliary routine (version 3.3.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*  -- April 2011                                                      --
*
*     .. Scalar Arguments ..
      CHARACTER          DIRECT, SIDE, STOREV, TRANS
      INTEGER            K, LDC, LDT, LDV, LDWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX            C( LDC, * ), T( LDT, * ), V( LDV, * ),
     $                   WORK( LDWORK, * )
*     ..
*
*  Purpose
*  =======
*
*  CLARFB applies a complex block reflector H or its transpose H**H to a
*  complex M-by-N matrix C, from either the left or the right.
*
*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply H or H**H from the Left
*          = 'R': apply H or H**H from the Right
*
*  TRANS   (input) CHARACTER*1
*          = 'N': apply H (No transpose)
*          = 'C': apply H**H (Conjugate 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) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) COMPLEX 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).
*
*  Further Details
*  ===============
*
*  The shape of the matrix V and the storage of the vectors which define
*  the H(i) is best illustrated by the following example with n = 5 and
*  k = 3. The elements equal to 1 are not stored; the corresponding
*  array elements are modified but restored on exit. The rest of the
*  array is not used.
*
*  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
*
*               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
*                   ( v1  1    )                     (     1 v2 v2 v2 )
*                   ( v1 v2  1 )                     (        1 v3 v3 )
*                   ( v1 v2 v3 )
*                   ( v1 v2 v3 )
*
*  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
*
*               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
*                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
*                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
*                   (     1 v3 )
*                   (        1 )
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ONE
      PARAMETER          ( ONE = ( 1.0E+00.0E+0 ) )
*     ..
*     .. Local Scalars ..
      CHARACTER          TRANST
      INTEGER            I, J, LASTV, LASTC
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILACLR, ILACLC
      EXTERNAL           LSAME, ILACLR, ILACLC
*     ..
*     .. External Subroutines ..
      EXTERNAL           CCOPY, CGEMM, CLACGV, CTRMM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CONJG
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( M.LE.0 .OR. N.LE.0 )
     $   RETURN
*
      IF( LSAME( TRANS, 'N' ) ) THEN
         TRANST = 'C'
      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**H * C  where  C = ( C1 )
*                                                    ( C2 )
*
               LASTV = MAX( K, ILACLR( M, K, V, LDV ) )
               LASTC = ILACLC( LASTV, N, C, LDC )
*
*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
*
*              W := C1**H
*
               DO 10 J = 1, K
                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
   10          CONTINUE
*
*              W := W * V1
*
               CALL CTRMM( 'Right''Lower''No transpose''Unit',
     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C2**H *V2
*
                  CALL CGEMM( 'Conjugate transpose''No transpose',
     $                 LASTC, K, LASTV-K, ONE, C( K+11 ), LDC,
     $                 V( K+11 ), LDV, ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**H  or  W * T
*
               CALL CTRMM( 'Right''Upper', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V * W**H
*
               IF( M.GT.K ) THEN
*
*                 C2 := C2 - V2 * W**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTV-K, LASTC, K, -ONE, V( K+11 ), LDV,
     $                 WORK, LDWORK, ONE, C( K+11 ), LDC )
               END IF
*
*              W := W * V1**H
*
               CALL CTRMM( 'Right''Lower''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
*
*              C1 := C1 - W**H
*
               DO 30 J = 1, K
                  DO 20 I = 1, LASTC
                     C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
   20             CONTINUE
   30          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
*
               LASTV = MAX( K, ILACLR( N, K, V, LDV ) )
               LASTC = ILACLR( M, LASTV, C, LDC )
*
*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
*
*              W := C1
*
               DO 40 J = 1, K
                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
   40          CONTINUE
*
*              W := W * V1
*
               CALL CTRMM( 'Right''Lower''No transpose''Unit',
     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C2 * V2
*
                  CALL CGEMM( 'No transpose''No transpose',
     $                 LASTC, K, LASTV-K,
     $                 ONE, C( 1, K+1 ), LDC, V( K+11 ), LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**H
*
               CALL CTRMM( 'Right''Upper', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V**H
*
               IF( LASTV.GT.K ) THEN
*
*                 C2 := C2 - W * V2**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTC, LASTV-K, K,
     $                 -ONE, WORK, LDWORK, V( K+11 ), LDV,
     $                 ONE, C( 1, K+1 ), LDC )
               END IF
*
*              W := W * V1**H
*
               CALL CTRMM( 'Right''Lower''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
*
*              C1 := C1 - W
*
               DO 60 J = 1, K
                  DO 50 I = 1, LASTC
                     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**H * C  where  C = ( C1 )
*                                                    ( C2 )
*
               LASTV = MAX( K, ILACLR( M, K, V, LDV ) )
               LASTC = ILACLC( LASTV, N, C, LDC )
*
*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
*
*              W := C2**H
*
               DO 70 J = 1, K
                  CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
     $                 WORK( 1, J ), 1 )
                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
   70          CONTINUE
*
*              W := W * V2
*
               CALL CTRMM( 'Right''Upper''No transpose''Unit',
     $              LASTC, K, ONE, V( LASTV-K+11 ), LDV,
     $              WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C1**H*V1
*
                  CALL CGEMM( 'Conjugate transpose''No transpose',
     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**H  or  W * T
*
               CALL CTRMM( 'Right''Lower', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V * W**H
*
               IF( LASTV.GT.K ) THEN
*
*                 C1 := C1 - V1 * W**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2**H
*
               CALL CTRMM( 'Right''Upper''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V( LASTV-K+11 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W**H
*
               DO 90 J = 1, K
                  DO 80 I = 1, LASTC
                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
     $                               CONJG( WORK( I, J ) )
   80             CONTINUE
   90          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
*
               LASTV = MAX( K, ILACLR( N, K, V, LDV ) )
               LASTC = ILACLR( M, LASTV, C, LDC )
*
*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK)
*
*              W := C2
*
               DO 100 J = 1, K
                  CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1,
     $                 WORK( 1, J ), 1 )
  100          CONTINUE
*
*              W := W * V2
*
               CALL CTRMM( 'Right''Upper''No transpose''Unit',
     $              LASTC, K, ONE, V( LASTV-K+11 ), LDV,
     $              WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C1 * V1
*
                  CALL CGEMM( 'No transpose''No transpose',
     $                 LASTC, K, LASTV-K,
     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**H
*
               CALL CTRMM( 'Right''Lower', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V**H
*
               IF( LASTV.GT.K ) THEN
*
*                 C1 := C1 - W * V1**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2**H
*
               CALL CTRMM( 'Right''Upper''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V( LASTV-K+11 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W
*
               DO 120 J = 1, K
                  DO 110 I = 1, LASTC
                     C( I, LASTV-K+J ) = C( I, LASTV-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**H * C  where  C = ( C1 )
*                                                    ( C2 )
*
               LASTV = MAX( K, ILACLC( K, M, V, LDV ) )
               LASTC = ILACLC( LASTV, N, C, LDC )
*
*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
*
*              W := C1**H
*
               DO 130 J = 1, K
                  CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
  130          CONTINUE
*
*              W := W * V1**H
*
               CALL CTRMM( 'Right''Upper''Conjugate transpose',
     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C2**H*V2**H
*
                  CALL CGEMM( 'Conjugate transpose',
     $                 'Conjugate transpose', LASTC, K, LASTV-K,
     $                 ONE, C( K+11 ), LDC, V( 1, K+1 ), LDV,
     $                 ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**H  or  W * T
*
               CALL CTRMM( 'Right''Upper', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V**H * W**H
*
               IF( LASTV.GT.K ) THEN
*
*                 C2 := C2 - V2**H * W**H
*
                  CALL CGEMM( 'Conjugate transpose',
     $                 'Conjugate transpose', LASTV-K, LASTC, K,
     $                 -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
     $                 ONE, C( K+11 ), LDC )
               END IF
*
*              W := W * V1
*
               CALL CTRMM( 'Right''Upper''No transpose''Unit',
     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
*
*              C1 := C1 - W**H
*
               DO 150 J = 1, K
                  DO 140 I = 1, LASTC
                     C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
  140             CONTINUE
  150          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
*
               LASTV = MAX( K, ILACLC( K, N, V, LDV ) )
               LASTC = ILACLR( M, LASTV, C, LDC )
*
*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
*
*              W := C1
*
               DO 160 J = 1, K
                  CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
  160          CONTINUE
*
*              W := W * V1**H
*
               CALL CTRMM( 'Right''Upper''Conjugate transpose',
     $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C2 * V2**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
     $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**H
*
               CALL CTRMM( 'Right''Upper', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V
*
               IF( LASTV.GT.K ) THEN
*
*                 C2 := C2 - W * V2
*
                  CALL CGEMM( 'No transpose''No transpose',
     $                 LASTC, LASTV-K, K,
     $                 -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
     $                 ONE, C( 1, K+1 ), LDC )
               END IF
*
*              W := W * V1
*
               CALL CTRMM( 'Right''Upper''No transpose''Unit',
     $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
*
*              C1 := C1 - W
*
               DO 180 J = 1, K
                  DO 170 I = 1, LASTC
                     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**H * C  where  C = ( C1 )
*                                                    ( C2 )
*
               LASTV = MAX( K, ILACLC( K, M, V, LDV ) )
               LASTC = ILACLC( LASTV, N, C, LDC )
*
*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
*
*              W := C2**H
*
               DO 190 J = 1, K
                  CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
     $                 WORK( 1, J ), 1 )
                  CALL CLACGV( LASTC, WORK( 1, J ), 1 )
  190          CONTINUE
*
*              W := W * V2**H
*
               CALL CTRMM( 'Right''Lower''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
     $              WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C1**H * V1**H
*
                  CALL CGEMM( 'Conjugate transpose',
     $                 'Conjugate transpose', LASTC, K, LASTV-K,
     $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
               END IF
*
*              W := W * T**H  or  W * T
*
               CALL CTRMM( 'Right''Lower', TRANST, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - V**H * W**H
*
               IF( LASTV.GT.K ) THEN
*
*                 C1 := C1 - V1**H * W**H
*
                  CALL CGEMM( 'Conjugate transpose',
     $                 'Conjugate transpose', LASTV-K, LASTC, K,
     $                 -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
               END IF
*
*              W := W * V2
*
               CALL CTRMM( 'Right''Lower''No transpose''Unit',
     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
     $              WORK, LDWORK )
*
*              C2 := C2 - W**H
*
               DO 210 J = 1, K
                  DO 200 I = 1, LASTC
                     C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
     $                               CONJG( WORK( I, J ) )
  200             CONTINUE
  210          CONTINUE
*
            ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
*
               LASTV = MAX( K, ILACLC( K, N, V, LDV ) )
               LASTC = ILACLR( M, LASTV, C, LDC )
*
*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
*
*              W := C2
*
               DO 220 J = 1, K
                  CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1,
     $                 WORK( 1, J ), 1 )
  220          CONTINUE
*
*              W := W * V2**H
*
               CALL CTRMM( 'Right''Lower''Conjugate transpose',
     $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
     $              WORK, LDWORK )
               IF( LASTV.GT.K ) THEN
*
*                 W := W + C1 * V1**H
*
                  CALL CGEMM( 'No transpose''Conjugate transpose',
     $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,
     $                 WORK, LDWORK )
               END IF
*
*              W := W * T  or  W * T**H
*
               CALL CTRMM( 'Right''Lower', TRANS, 'Non-unit',
     $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
*
*              C := C - W * V
*
               IF( LASTV.GT.K ) THEN
*
*                 C1 := C1 - W * V1
*
                  CALL CGEMM( 'No transpose''No transpose',
     $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
     $                 ONE, C, LDC )
               END IF
*
*              W := W * V2
*
               CALL CTRMM( 'Right''Lower''No transpose''Unit',
     $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
     $              WORK, LDWORK )
*
*              C1 := C1 - W
*
               DO 240 J = 1, K
                  DO 230 I = 1, LASTC
                     C( I, LASTV-K+J ) = C( I, LASTV-K+J )
     $                    - WORK( I, J )
  230             CONTINUE
  240          CONTINUE
*
            END IF
*
         END IF
      END IF
*
      RETURN
*
*     End of CLARFB
*
      END