!!$
!!$
!!$ MLD2P4 version 1.0
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 2.2)
!!$
!!$ (C) Copyright 2008
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari University of Rome Tor Vergata
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$
!!$ Redistribution and use in source and binary forms, with or without
!!$ modification, are permitted provided that the following conditions
!!$ are met:
!!$ 1. Redistributions of source code must retain the above copyright
!!$ notice, this list of conditions and the following disclaimer.
!!$ 2. Redistributions in binary form must reproduce the above copyright
!!$ notice, this list of conditions, and the following disclaimer in the
!!$ documentation and/or other materials provided with the distribution.
!!$ 3. The name of the MLD2P4 group or the names of its contributors may
!!$ not be used to endorse or promote products derived from this
!!$ software without specific written permission.
!!$
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
!!$ POSSIBILITY OF SUCH DAMAGE.
!!$
!!$
! File: mld_daggrmap_bld.f90
!
! Subroutine: mld_daggrmap_bld
! Version: real
!
! This routine builds a mapping from the row indices of the fine-level matrix
! to the row indices of the coarse-level matrix, according to a decoupled
! aggregation algorithm. This mapping will be used by mld_aggrmat_asb to
! build the coarse-level matrix.
!
! The aggregation algorithm is a parallel version of that described in
! * M. Brezina and P. Vanek, A black-box iterative solver based on a
! two-level Schwarz method, Computing, 63 (1999), 233-263.
! * P. Vanek, J. Mandel and M. Brezina, Algebraic Multigrid by Smoothed
! Aggregation for Second and Fourth Order Elliptic Problems, Computing, 56
! (1996), 179-196.
! For more details see
! P. D'Ambra, D. di Serafino and S. Filippone, On the development of
! PSBLAS-based parallel two-level Schwarz preconditioners, Appl. Num. Math.
! 57 (2007), 1181-1196.
!
!
! Arguments:
! aggr_type - integer, input.
! The scalar used to identify the aggregation algorithm.
! theta - real, input.
! The aggregation threshold used in the aggregation algorithm.
! a - type(psb_dspmat_type), input.
! The sparse matrix structure containing the local part of
! the fine-level matrix.
! desc_a - type(psb_desc_type), input.
! The communication descriptor of the fine-level matrix.
! nlaggr - integer, dimension(:), allocatable.
! nlaggr(i) contains the aggregates held by process i.
! ilaggr - integer, dimension(:), allocatable.
! The mapping between the row indices of the coarse-level
! matrix and the row indices of the fine-level matrix.
! ilaggr(i)=j means that node i in the adjacency graph
! of the fine-level matrix is mapped onto node j in the
! adjacency graph of the coarse-level matrix.
! info - integer, output.
! Error code.
!
subroutine mld_daggrmap_bld(aggr_type,theta,a,desc_a,nlaggr,ilaggr,info)
use psb_base_mod
use mld_inner_mod, mld_protect_name => mld_daggrmap_bld
implicit none
! Arguments
integer, intent(in) :: aggr_type
real(psb_dpk_), intent(in) :: theta
type(psb_dspmat_type), intent(in) :: a
type(psb_desc_type), intent(in) :: desc_a
integer, allocatable, intent(out) :: ilaggr(:),nlaggr(:)
integer, intent(out) :: info
! Local variables
integer, allocatable :: ils(:), neigh(:)
integer :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m
type(psb_dspmat_type) :: atmp, atrans
logical :: recovery
integer :: debug_level, debug_unit
integer :: ictxt,np,me,err_act
integer :: nrow, ncol, n_ne
character(len=20) :: name, ch_err
if(psb_get_errstatus() /= 0) return
info=0
name = 'mld_aggrmap_bld'
call psb_erractionsave(err_act)
debug_unit = psb_get_debug_unit()
debug_level = psb_get_debug_level()
!
ictxt=psb_cd_get_context(desc_a)
call psb_info(ictxt,me,np)
nrow = psb_cd_get_local_rows(desc_a)
ncol = psb_cd_get_local_cols(desc_a)
select case (aggr_type)
case (mld_dec_aggr_)
call mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info)
case (mld_sym_dec_aggr_)
nr = psb_sp_get_nrows(a)
call psb_sp_clip(a,atmp,info,imax=nr,jmax=nr,&
& rscale=.false.,cscale=.false.)
atmp%m=nr
atmp%k=nr
if (info == 0) call psb_transp(atmp,atrans,fmt='COO')
if (info == 0) call psb_rwextd(nr,atmp,info,b=atrans,rowscale=.false.)
atmp%m=nr
atmp%k=nr
if (info == 0) call psb_sp_free(atrans,info)
if (info == 0) call psb_ipcoo2csr(atmp,info)
if (info == 0) call mld_dec_map_bld(theta,atmp,desc_a,nlaggr,ilaggr,info)
if (info == 0) call psb_sp_free(atmp,info)
case default
info = -1
call psb_errpush(30,name,i_err=(/1,aggr_type,0,0,0/))
goto 9999
end select
if (info/=0) then
info=4001
call psb_errpush(info,name,a_err='dec_map_bld')
goto 9999
end if
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act.eq.psb_act_abort_) then
call psb_error()
return
end if
return
contains
subroutine mld_dec_map_bld(theta,a,desc_a,nlaggr,ilaggr,info)
use psb_base_mod
use mld_inner_mod !, mld_protect_name => mld_daggrmap_bld
implicit none
! Arguments
type(psb_dspmat_type), intent(in) :: a
type(psb_desc_type), intent(in) :: desc_a
real(psb_dpk_), intent(in) :: theta
integer, allocatable, intent(out) :: ilaggr(:),nlaggr(:)
integer, intent(out) :: info
! Local variables
integer, allocatable :: ils(:), neigh(:), irow(:), icol(:)
real(psb_dpk_), allocatable :: val(:), diag(:)
integer :: icnt,nlp,k,n,ia,isz,nr, naggr,i,j,m, nz
real(psb_dpk_) :: cpling, tcl
logical :: recovery
integer :: debug_level, debug_unit
integer :: ictxt,np,me,err_act
integer :: nrow, ncol, n_ne
character(len=20) :: name, ch_err
if(psb_get_errstatus() /= 0) return
info=0
name = 'mld_dec_map_bld'
call psb_erractionsave(err_act)
debug_unit = psb_get_debug_unit()
debug_level = psb_get_debug_level()
!
ictxt=psb_cd_get_context(desc_a)
call psb_info(ictxt,me,np)
nrow = psb_cd_get_local_rows(desc_a)
ncol = psb_cd_get_local_cols(desc_a)
nr = a%m
allocate(ilaggr(nr),neigh(nr),stat=info)
if(info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/2*nr,0,0,0,0/),&
& a_err='integer')
goto 9999
end if
allocate(diag(nr),stat=info)
if(info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/nr,0,0,0,0/),&
& a_err='real(psb_dpk_)')
goto 9999
end if
call psb_sp_getdiag(a,diag,info)
if(info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_sp_getdiag')
goto 9999
end if
do i=1, nr
ilaggr(i) = -(nr+1)
end do
! Note: -(nr+1) Untouched as yet
! -i 1<=i<=nr Adjacent to aggregate i
! i 1<=i<=nr Belonging to aggregate i
!
! Phase one: group nodes together.
! Very simple minded strategy.
!
naggr = 0
nlp = 0
do
icnt = 0
do i=1, nr
if (ilaggr(i) == -(nr+1)) then
!
! 1. Untouched nodes are marked >0 together
! with their neighbours
!
icnt = icnt + 1
naggr = naggr + 1
ilaggr(i) = naggr
call psb_sp_getrow(i,a,nz,irow,icol,val,info)
if (info/=0) then
info=4010
call psb_errpush(info,name,a_err='psb_sp_getrow')
goto 9999
end if
do k=1, nz
j = icol(k)
if ((1<=j).and.(j<=nr).and.(i/=j)) then
if (abs(val(k)) > theta*sqrt(abs(diag(i)*diag(j)))) then
ilaggr(j) = naggr
else
ilaggr(j) = -naggr
endif
end if
enddo
!
! 2. Untouched neighbours of these nodes are marked <0.
!
call psb_neigh(a,i,neigh,n_ne,info,lev=2)
if (info/=0) then
info=4010
call psb_errpush(info,name,a_err='psb_neigh')
goto 9999
end if
do n = 1, n_ne
m = neigh(n)
if ((1<=m).and.(m<=nr)) then
if (ilaggr(m) == -(nr+1)) ilaggr(m) = -naggr
endif
enddo
endif
enddo
nlp = nlp + 1
if (icnt == 0) exit
enddo
if (debug_level >= psb_debug_outer_) then
write(debug_unit,*) me,' ',trim(name),&
& ' Check 1:',count(ilaggr == -(nr+1)),&
& (a%ia1(i),i=a%ia2(1),a%ia2(2)-1)
end if
!
! Phase two: sweep over leftovers.
!
allocate(ils(nr),stat=info)
if(info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/naggr+10,0,0,0,0/),&
& a_err='integer')
goto 9999
end if
do i=1, size(ils)
ils(i) = 0
end do
do i=1, nr
n = ilaggr(i)
if (n>0) then
if (n>naggr) then
info=4001
call psb_errpush(info,name,a_err='loc_Aggregate: n > naggr 1 ?')
goto 9999
else
ils(n) = ils(n) + 1
end if
end if
end do
if (debug_level >= psb_debug_outer_) then
write(debug_unit,*) me,' ',trim(name),&
& 'Phase 1: number of aggregates ',naggr
write(debug_unit,*) me,' ',trim(name),&
& 'Phase 1: nodes aggregated ',sum(ils)
end if
recovery=.false.
do i=1, nr
if (ilaggr(i) < 0) then
!
! Now some silly rule to break ties:
! Group with adjacent aggregate.
!
isz = nr+1
ia = -1
cpling = 0.0d0
call psb_sp_getrow(i,a,nz,irow,icol,val,info)
if (info/=0) then
info=4010
call psb_errpush(info,name,a_err='psb_sp_getrow')
goto 9999
end if
do j=1, nz
k = icol(j)
if ((1<=k).and.(k<=nr).and.(k/=i)) then
tcl = abs(val(j)) / sqrt(abs(diag(i)*diag(k)))
if (abs(val(j)) > theta*sqrt(abs(diag(i)*diag(k)))) then
!!$ if (tcl > theta) then
n = ilaggr(k)
if (n>0) then
if (n>naggr) then
info=4001
call psb_errpush(info,name,a_err='loc_Aggregate: n > naggr 2 ?')
goto 9999
end if
if ((abs(val(j))>cpling) .or. &
& ((abs(val(j)) == cpling).and. (ils(n) < isz))) then
!!$ if ((tcl > cpling) .or. ((tcl == cpling).and. (ils(n) < isz))) then
ia = n
isz = ils(n)
cpling = abs(val(j))
!!$ cpling = tcl
endif
endif
endif
end if
enddo
if (ia == -1) then
! At this point, the easiest thing is to start a new aggregate
naggr = naggr + 1
ilaggr(i) = naggr
ils(ilaggr(i)) = 1
else
ilaggr(i) = ia
if (ia>naggr) then
info=4001
call psb_errpush(info,name,a_err='loc_Aggregate: n > naggr 4? ')
goto 9999
end if
ils(ia) = ils(ia) + 1
endif
end if
end do
if (debug_level >= psb_debug_outer_) then
if (recovery) then
write(debug_unit,*) me,' ',trim(name),&
& 'Had to recover from strange situation in loc_aggregate.'
write(debug_unit,*) me,' ',trim(name),&
& 'Perhaps an unsymmetric pattern?'
endif
write(debug_unit,*) me,' ',trim(name),&
& 'Phase 2: number of aggregates ',naggr,sum(ils)
do i=1, naggr
write(debug_unit,*) me,' ',trim(name),&
& 'Size of aggregate ',i,' :',count(ilaggr==i), ils(i)
enddo
write(debug_unit,*) me,' ',trim(name),&
& maxval(ils(1:naggr))
write(debug_unit,*) me,' ',trim(name),&
& 'Leftovers ',count(ilaggr<0), ' in ',nlp,' loops'
end if
if (count(ilaggr<0) >0) then
info=4001
call psb_errpush(info,name,a_err='Fatal error: some leftovers')
goto 9999
endif
deallocate(ils,neigh,stat=info)
if (info/=0) then
info=4000
call psb_errpush(info,name)
goto 9999
end if
if (naggr > ncol) then
write(0,*) name,'Error : naggr > ncol',naggr,ncol
info=4001
call psb_errpush(info,name,a_err='Fatal error: naggr>ncol')
goto 9999
end if
call psb_realloc(ncol,ilaggr,info)
if (info/=0) then
info=4010
ch_err='psb_realloc'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
allocate(nlaggr(np),stat=info)
if (info/=0) then
info=4025
call psb_errpush(info,name,i_err=(/np,0,0,0,0/),&
& a_err='integer')
goto 9999
end if
nlaggr(:) = 0
nlaggr(me+1) = naggr
call psb_sum(ictxt,nlaggr(1:np))
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act.eq.psb_act_abort_) then
call psb_error()
return
end if
return
end subroutine mld_dec_map_bld
end subroutine mld_daggrmap_bld