!!$ !!$ !!$ 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,ilaggr,nlaggr,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_spcnv(atmp,info,afmt='csr') 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