```      SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*     .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER TRANS
*     ..
*     .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
*     ..
*
*  Purpose
*  =======
*
*  ZGBMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   or
*
*     y := alpha*conjg( A' )*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n band matrix, with kl sub-diagonals and ku super-diagonals.
*
*  Arguments
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*conjg( A' )*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  KL     - INTEGER.
*           On entry, KL specifies the number of sub-diagonals of the
*           matrix A. KL must satisfy  0 .le. KL.
*           Unchanged on exit.
*
*  KU     - INTEGER.
*           On entry, KU specifies the number of super-diagonals of the
*           matrix A. KU must satisfy  0 .le. KU.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry, the leading ( kl + ku + 1 ) by n part of the
*           array A must contain the matrix of coefficients, supplied
*           column by column, with the leading diagonal of the matrix in
*           row ( ku + 1 ) of the array, the first super-diagonal
*           starting at position 2 in row ku, the first sub-diagonal
*           starting at position 1 in row ( ku + 2 ), and so on.
*           Elements in the array A that do not correspond to elements
*           in the band matrix (such as the top left ku by ku triangle)
*           are not referenced.
*           The following program segment will transfer a band matrix
*           from conventional full matrix storage to band storage:
*
*                 DO 20, J = 1, N
*                    K = KU + 1 - J
*                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
*                       A( K + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( kl + ku + 1 ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry, the incremented array Y must contain the
*           vector y. On exit, Y is overwritten by the updated vector y.
*
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
*     ..
*     .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
LOGICAL NOCONJ
*     ..
*     .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX,MIN
*     ..
*
*     Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+    .NOT.LSAME(TRANS,'C')) THEN
INFO = 1
ELSE IF (M.LT.0) THEN
INFO = 2
ELSE IF (N.LT.0) THEN
INFO = 3
ELSE IF (KL.LT.0) THEN
INFO = 4
ELSE IF (KU.LT.0) THEN
INFO = 5
ELSE IF (LDA.LT. (KL+KU+1)) THEN
INFO = 8
ELSE IF (INCX.EQ.0) THEN
INFO = 10
ELSE IF (INCY.EQ.0) THEN
INFO = 13
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZGBMV ',INFO)
RETURN
END IF
*
*     Quick return if possible.
*
IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
+    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
*
NOCONJ = LSAME(TRANS,'T')
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
IF (LSAME(TRANS,'N')) THEN
LENX = N
LENY = M
ELSE
LENX = M
LENY = N
END IF
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (LENX-1)*INCX
END IF
IF (INCY.GT.0) THEN
KY = 1
ELSE
KY = 1 - (LENY-1)*INCY
END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the band part of A.
*
*     First form  y := beta*y.
*
IF (BETA.NE.ONE) THEN
IF (INCY.EQ.1) THEN
IF (BETA.EQ.ZERO) THEN
DO 10 I = 1,LENY
Y(I) = ZERO
10             CONTINUE
ELSE
DO 20 I = 1,LENY
Y(I) = BETA*Y(I)
20             CONTINUE
END IF
ELSE
IY = KY
IF (BETA.EQ.ZERO) THEN
DO 30 I = 1,LENY
Y(IY) = ZERO
IY = IY + INCY
30             CONTINUE
ELSE
DO 40 I = 1,LENY
Y(IY) = BETA*Y(IY)
IY = IY + INCY
40             CONTINUE
END IF
END IF
END IF
IF (ALPHA.EQ.ZERO) RETURN
KUP1 = KU + 1
IF (LSAME(TRANS,'N')) THEN
*
*        Form  y := alpha*A*x + y.
*
JX = KX
IF (INCY.EQ.1) THEN
DO 60 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*X(JX)
K = KUP1 - J
DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
Y(I) = Y(I) + TEMP*A(K+I,J)
50                 CONTINUE
END IF
JX = JX + INCX
60         CONTINUE
ELSE
DO 80 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*X(JX)
IY = KY
K = KUP1 - J
DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
Y(IY) = Y(IY) + TEMP*A(K+I,J)
IY = IY + INCY
70                 CONTINUE
END IF
JX = JX + INCX
IF (J.GT.KU) KY = KY + INCY
80         CONTINUE
END IF
ELSE
*
*        Form  y := alpha*A'*x + y  or  y := alpha*conjg( A' )*x + y.
*
JY = KY
IF (INCX.EQ.1) THEN
DO 110 J = 1,N
TEMP = ZERO
K = KUP1 - J
IF (NOCONJ) THEN
DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
TEMP = TEMP + A(K+I,J)*X(I)
90                 CONTINUE
ELSE
DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
100                 CONTINUE
END IF
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
110         CONTINUE
ELSE
DO 140 J = 1,N
TEMP = ZERO
IX = KX
K = KUP1 - J
IF (NOCONJ) THEN
DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
TEMP = TEMP + A(K+I,J)*X(IX)
IX = IX + INCX
120                 CONTINUE
ELSE
DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
IX = IX + INCX
130                 CONTINUE
END IF
Y(JY) = Y(JY) + ALPHA*TEMP
JY = JY + INCY
IF (J.GT.KU) KX = KX + INCX
140         CONTINUE
END IF
END IF
*
RETURN
*
*     End of ZGBMV .
*
END

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