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spclibs/pppack/subbak.f90
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subbak.f90
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!>
!> @file subbak.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 subbak ( w, ipivot, nrow, ncol, last, x )
!*************************************************************************
!
!! SUBBAK carries out backsubstitution for the current block.
!
! Reference:
!
! Carl DeBoor,
! A Practical Guide to Splines,
! Springer Verlag.
!
! Parameters:
!
! w, ipivot, nrow, ncol, last are as on return from factrb.
!
! x(1),...,x(ncol) contains, on input, the right side for the
! equations in this block after backsubstitution has been
! carried up to but not including equation ipivot(last).
! means that x(j) contains the right side of equation ipi-
! vot(j) as modified during elimination, j=1,...,last, while
! for j > last, x(j) is already a component of the solut-
! ion vector.
!
! x(1),...,x(ncol) contains, on output, the components of the solut-
! ion corresponding to the present block.
!
implicit none
integer ncol
integer nrow
integer ip
integer ipivot(nrow)
integer j
integer k
integer last
real ( kind = 8 ) s
real ( kind = 8 ) w(nrow,ncol)
real ( kind = 8 ) x(ncol)
do k = last, 1, -1
ip = ipivot(k)
s = 0.0D+00
do j = k+1, ncol
s = s + w(ip,j) * x(j)
end do
x(k) = ( x(k) - s ) / w(ip,k)
end do
end
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