!>
!> @file fcblok.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 fcblok ( bloks, integs, nbloks, ipivot, scrtch, iflag )

!*************************************************************************
!
!! FCBLOK supervises the PLU factorization with pivoting of
!  scaled rows of the almost block diagonal matrix.
!
!    The almost block diagonal matrix is stored in the arrays
!    BLOKS and INTEGS.
!
!    The FACTRB routine carries out steps 1,...,last of gauss
!    elimination (with pivoting) for an individual block.
!
!    The SHIFTB routine shifts the remaining rows to the top of
!    the next block
!
!  Reference:
!
!    Carl DeBoor,
!    A Practical Guide to Splines,
!    Springer Verlag.
!
!  Parameters:
!
!  bloks   an array that initially contains the almost block diagonal
!            matrix  a  to be factored, and on return contains the com-
!            puted factorization of  a .
!
!  integs  an integer array describing the block structure of  a .
!
!  nbloks  the number of blocks in  a .
!
!  ipivot  an integer array of dimension  sum (integs(1,n) ; n=1,
!            ...,nbloks) which, on return, contains the pivoting stra-
!            tegy used.
!
!  scrtch  work area required, of length  max (integs(1,n) ; n=1,
!            ...,nbloks).
!
!  iflag   output parameter;
!          =0  in case matrix was found to be singular.
!            otherwise,
!          =(-1)**(number of row interchanges during factorization)
!
  implicit none

  integer nbloks

  real ( kind = 8 ) bloks(*)
  integer i
  integer iflag
  integer index
  integer indexb
  integer indexn
  integer integs(3,nbloks)
  integer ipivot(*)
  integer last
  integer ncol
  integer nrow
  real ( kind = 8 ) scrtch(*)

  iflag = 1
  indexb = 1
  indexn = 1
  i = 1
!
!  Loop over the blocks.  i  is loop index
!
  do

    index = indexn
    nrow = integs(1,i)
    ncol = integs(2,i)
    last = integs(3,i)
!
!  Carry out elimination on the I-th block until next block
!  enters, for columns 1 through LAST of I-th block.
!
    call factrb ( bloks(index), ipivot(indexb), scrtch, nrow, ncol, &
      last, iflag )
!
!  Check for having reached a singular block or the last block.
!
    if ( iflag == 0 .or. i == nbloks ) then
      exit
    end if

    i = i + 1
    indexn = nrow * ncol + index
!
!  Put the rest of the I-th block onto the next block.
!
    call shiftb ( bloks(index), ipivot(indexb), nrow, ncol, last, &
      bloks(indexn), integs(1,i), integs(2,i) )

    indexb = indexb + nrow

  end do

  return
end