!>
!> @file sbblok.f90
!>
!> @brief
!>
!> @copyright
!> Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
!> SPC (Swiss Plasma Center)
!>
!> SPClibs is free software: you can redistribute it and/or modify it under
!> the terms of the GNU Lesser General Public License as published by the Free
!> Software Foundation, either version 3 of the License, or (at your option)
!> any later version.
!>
!> SPClibs is distributed in the hope that it will be useful, but WITHOUT ANY
!> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
!> FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!>
!> You should have received a copy of the GNU Lesser General Public License
!> along with this program. If not, see <https://www.gnu.org/licenses/>.
!>
!> @author
!> (in alphabetical order)
!> @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
!>
subroutine sbblok ( bloks, integs, nbloks, ipivot, b, x )

!*************************************************************************
!
!! 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.
!
!  Reference:
!
!    Carl DeBoor,
!    A Practical Guide to Splines,
!    Springer Verlag.
!
!  Parameters:
!
!    bloks, integs, nbloks, ipivot    are as on return from fcblok.
!
!    b       the right 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 nbloks

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