subroutine zgbmv ( trans, m, n, kl, ku, alpha, a, lda, x, incx,
     $                   beta, y, incy )
*     .. scalar arguments ..
      complex*16         alpha, beta
      integer            incx, incy, kl, ku, lda, m, n
      character*1        trans
*     .. array arguments ..
      complex*16         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.
*
*  parameters
*  ==========
*
*  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.
*