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spclibs/pppack/subfor.f90
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subfor.f90
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!>
!> @file subfor.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 subfor ( w, ipivot, nrow, last, b, x )
!*************************************************************************
!
!! SUBFOR carries out the forward pass of substitution for the current block.
!
! Discussion:
!
! The forward pass is the action on the right side corresponding to the
! elimination carried out in FACTRB for this block.
!
! At the end, x(j) contains the right side of the transformed
! ipivot(j)-th equation in this block, j=1,...,nrow. then, since
! for i=1,...,nrow-last, b(nrow+i) is going to be used as the right
! side of equation I in the next block (shifted over there from
! this block during factorization), it is set equal to x(last+i) here.
!
! Reference:
!
! Carl DeBoor,
! A Practical Guide to Splines,
! Springer Verlag.
!
! Parameters:
!
! w, ipivot, nrow, last are as on return from factrb.
!
! b(j) is expected to contain, on input, the right side of j-th
! equation for this block, j=1,...,nrow.
! b(nrow+j) contains, on output, the appropriately modified right
! side for equation j in next block, j=1,...,nrow-last.
!
! x(j) contains, on output, the appropriately modified right
! side of equation ipivot(j) in this block, j=1,...,last (and
! even for j=last+1,...,nrow).
!
implicit none
integer last
integer nrow
real ( kind = 8 ) b(nrow+nrow-last)
integer ip
integer ipivot(nrow)
integer j
integer k
real ( kind = 8 ) s
real ( kind = 8 ) w(nrow,last)
real ( kind = 8 ) x(nrow)
ip = ipivot(1)
x(1) = b(ip)
do k = 2, nrow
ip = ipivot(k)
s = 0.0D+00
do j = 1, min ( k-1, last )
s = s + w(ip,j) * x(j)
end do
x(k) = b(ip) - s
end do
!
! Transfer modified right sides of equations ipivot(last+1),...,
! ipivot(nrow) to next block.
!
do k = last+1, nrow
b(nrow-last+k) = x(k)
end do
return
end
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