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fcblok.f90
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!>
!> @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
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