subroutine stbmv ( uplo, trans, diag, n, k, a, lda, x, incx )
*     .. scalar arguments ..
      integer            incx, k, lda, n
      character*1        diag, trans, uplo
*     .. array arguments ..
      real               a( lda, * ), x( * )
*     ..
*
*  purpose
*  =======
*
*  stbmv  performs one of the matrix-vector operations
*
*     x := a*x,   or   x := a'*x,
*
*  where x is an n element vector and  a is an n by n unit, or non-unit,
*  upper or lower triangular band matrix, with ( k + 1 ) diagonals.
*
*  parameters
*  ==========
*
*  uplo   - character*1.
*           on entry, uplo specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              uplo = 'u' or 'u'   a is an upper triangular matrix.
*
*              uplo = 'l' or 'l'   a is a lower triangular matrix.
*
*           unchanged on exit.
*
*  trans  - character*1.
*           on entry, trans specifies the operation to be performed as
*           follows:
*
*              trans = 'n' or 'n'   x := a*x.
*
*              trans = 't' or 't'   x := a'*x.
*
*              trans = 'c' or 'c'   x := a'*x.
*
*           unchanged on exit.
*
*  diag   - character*1.
*           on entry, diag specifies whether or not a is unit
*           triangular as follows:
*
*              diag = 'u' or 'u'   a is assumed to be unit triangular.
*
*              diag = 'n' or 'n'   a is not assumed to be unit
*                                  triangular.
*
*           unchanged on exit.
*
*  n      - integer.
*           on entry, n specifies the order of the matrix a.
*           n must be at least zero.
*           unchanged on exit.
*
*  k      - integer.
*           on entry with uplo = 'u' or 'u', k specifies the number of
*           super-diagonals of the matrix a.
*           on entry with uplo = 'l' or 'l', k specifies the number of
*           sub-diagonals of the matrix a.
*           k must satisfy  0 .le. k.
*           unchanged on exit.
*
*  a      - real             array of dimension ( lda, n ).
*           before entry with uplo = 'u' or 'u', the leading ( k + 1 )
*           by n part of the array a must contain the upper triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row
*           ( k + 1 ) of the array, the first super-diagonal starting at
*           position 2 in row k, and so on. the top left k by k triangle
*           of the array a is not referenced.
*           the following program segment will transfer an upper
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 do 20, j = 1, n
*                    m = k + 1 - j
*                    do 10, i = max( 1, j - k ), j
*                       a( m + i, j ) = matrix( i, j )
*              10    continue
*              20 continue
*
*           before entry with uplo = 'l' or 'l', the leading ( k + 1 )
*           by n part of the array a must contain the lower triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row 1 of
*           the array, the first sub-diagonal starting at position 1 in
*           row 2, and so on. the bottom right k by k triangle of the
*           array a is not referenced.
*           the following program segment will transfer a lower
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 do 20, j = 1, n
*                    m = 1 - j
*                    do 10, i = j, min( n, j + k )
*                       a( m + i, j ) = matrix( i, j )
*              10    continue
*              20 continue
*
*           note that when diag = 'u' or 'u' the elements of the array a
*           corresponding to the diagonal elements of the matrix are not
*           referenced, but are assumed to be unity.
*           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
*           ( k + 1 ).
*           unchanged on exit.
*
*  x      - real             array of dimension at least
*           ( 1 + ( n - 1 )*abs( incx ) ).
*           before entry, the incremented array x must contain the n
*           element vector x. on exit, x is overwritten with the
*           tranformed vector x.
*
*  incx   - integer.
*           on entry, incx specifies the increment for the elements of
*           x. incx 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.
*