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spclibs/pppack/sbblok.f90
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sbblok.f90
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!>
!> @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
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