banslv Subroutine

subroutine banslv ( w, nroww, nrow, nbandl, nbandu, b )

  !*****************************************************************************80
  !
  !! BANSLV solves a banded linear system A * X = B factored by BANFAC.
  !
  !  Modified:
  !
  !    14 February 2007
  !
  !  Author:
  !
  !    Carl DeBoor
  !
  !  Reference:
  !
  !    Carl DeBoor,
  !    A Practical Guide to Splines,
  !    Springer, 2001,
  !    ISBN: 0387953663,
  !    LC: QA1.A647.v27.
  !
  !  Parameters:
  !
  !    Input, real ( kind = 8 ) W(NROWW,NROW).  W contains the banded matrix,
  !    after it has been factored by BANFAC.
  !
  !    Input, integer ( kind = 4 ) NROWW, the row dimension of the work array W.
  !    NROWW must be at least NBANDL+1 + NBANDU.
  ! 
  !    Input, integer ( kind = 4 ) NROW, the number of rows in A.
  !
  !    Input, integer ( kind = 4 ) NBANDL, the number of bands of A below the 
  !    main diagonal.
  ! 
  !    Input, integer ( kind = 4 ) NBANDU, the number of bands of A above the 
  !    main diagonal.
  ! 
  !    Input/output, real ( kind = 8 ) B(NROW).
  !    On input, B contains the right hand side of the system to be solved.
  !    On output, B contains the solution, X.
  !
  implicit none

  integer ( kind = 4 ) nrow
  integer ( kind = 4 ) nroww

  real ( kind = 8 ) b(nrow)
  integer ( kind = 4 ) i
  integer ( kind = 4 ) j
  integer ( kind = 4 ) jmax
  integer ( kind = 4 ) middle
  integer ( kind = 4 ) nbandl
  integer ( kind = 4 ) nbandu
  real ( kind = 8 ) w(nroww,nrow)

  middle = nbandu + 1

  if ( nrow == 1 ) then
     b(1) = b(1) / w(middle,1)
     return
  end if
  !
  !  Forward pass:
  !
  !  For I = 1, 2, ..., NROW-1, subtract RHS(I)*(I-th column of L) 
  !  from the right hand side, below the I-th row.
  !
  if ( 0 < nbandl ) then
     do i = 1, nrow-1
        jmax = min ( nbandl, nrow-i )
        do j = 1, jmax
           b(i+j) = b(i+j) - b(i) * w(middle+j,i)
        end do
     end do
  end if
  !
  !  Backward pass:
  !
  !  For I=NROW, NROW-1,...,1, divide RHS(I) by 
  !  the I-th diagonal entry of U, then subtract 
  !  RHS(I)*(I-th column of U) from right hand side, above the I-th row.
  !
  do i = nrow, 2, -1

     b(i) = b(i) / w(middle,i)

     do j = 1, min ( nbandu, i-1 )
        b(i-j) = b(i-j) - b(i) * w(middle-j,i)
     end do

  end do

  b(1) = b(1) / w(middle,1)

  return
end subroutine banslv