sbblok Subroutine

subroutine sbblok ( bloks, integs, nbloks, ipivot, b, x )

  !*****************************************************************************80
  !
  !! SBBLOK solves a linear system that was factored by FCBLOK.
  !
  !  Discussion:
  !
  !    The routine supervises the solution, by forward and backward 
  !    substitution, of the linear system 
  !
  !      A * x = b
  !
  !    for X, with the PLU factorization of A already generated in FCBLOK.
  !    Individual blocks of equations are solved via SUBFOR and SUBBAK.
  !
  !  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 ) BLOKS(*), integer INTEGS(3,NBLOKS), integer
  !    NBLOKS, integer IPIVOT(*), are as on return from FCBLOK.
  !
  !    Input, real ( kind = 8 ) B(*), the right hand side, stored corresponding 
  !    to the storage of the equations.  See comments in SLVBLK for details.
  !
  !    Output, real ( kind = 8 ) X(*), the solution vector.
  !
  implicit none

  integer ( kind = 4 ) nbloks

  real ( kind = 8 ) b(*)
  real ( kind = 8 ) bloks(*)
  integer ( kind = 4 ) i
  integer ( kind = 4 ) index
  integer ( kind = 4 ) indexb
  integer ( kind = 4 ) indexx
  integer ( kind = 4 ) integs(3,nbloks)
  integer ( kind = 4 ) ipivot(*)
  integer ( kind = 4 ) j
  integer ( kind = 4 ) last
  integer ( kind = 4 ) nbp1
  integer ( kind = 4 ) ncol
  integer ( kind = 4 ) nrow
  real ( kind = 8 ) x(*)
  !
  !  Forward substitution:
  !
  index = 1
  indexb = 1
  indexx = 1

  do i = 1, nbloks

     nrow = integs(1,i)
     last = integs(3,i)

     call subfor ( bloks(index), ipivot(indexb), nrow, last, b(indexb), &
          x(indexx) )

     index = nrow * integs(2,i) + index
     indexb = indexb + nrow
     indexx = indexx + last

  end do
  !
  !  Back substitution.
  !
  nbp1 = nbloks + 1

  do j = 1, nbloks

     i = nbp1 - j
     nrow = integs(1,i)
     ncol = integs(2,i)
     last = integs(3,i)
     index = index - nrow * ncol
     indexb = indexb - nrow
     indexx = indexx - last

     call subbak ( bloks(index), ipivot(indexb), nrow, ncol, last, x(indexx) )

  end do

  return
end subroutine sbblok