!!$ !!$ !!$ 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_saggrmat_smth_asb.F90 ! ! Subroutine: mld_saggrmat_smth_asb ! Version: real ! ! This routine builds a coarse-level matrix A_C from a fine-level matrix A ! by using a Galerkin approach, i.e. ! ! A_C = P_C^T A P_C, ! ! where P_C is a prolongator from the coarse level to the fine one. ! ! The prolongator P_C is built according to a smoothed aggregation algorithm, ! i.e. it is obtained by applying a damped Jacobi smoother to the piecewise ! constant interpolation operator P corresponding to the fine-to-coarse level ! mapping built by the mld_aggrmap_bld subroutine: ! ! P_C = (I - omega*D^(-1)A) * P, ! ! where D is the diagonal matrix with main diagonal equal to the main diagonal ! of A, and omega is a suitable smoothing parameter. An estimate of the spectral ! radius of D^(-1)A, to be used in the computation of omega, is provided, ! according to the value of p%iprcparm(mld_aggr_omega_alg_), specified by the user ! through mld_sprecinit and mld_sprecset. ! ! This routine can also build A_C according to a "bizarre" aggregation algorithm, ! using a "naive" prolongator proposed by the authors of MLD2P4. However, this ! prolongator still requires a deep analysis and testing and its use is not ! recommended. ! ! The coarse-level matrix A_C is distributed among the parallel processes or ! replicated on each of them, according to the value of p%iprcparm(mld_coarse_mat_), ! specified by the user through mld_sprecinit and mld_sprecset. ! ! For more details see ! M. Brezina and P. Vanek, A black-box iterative solver based on a ! two-level Schwarz method, Computing, 63 (1999), 233-263. ! 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: ! a - type(psb_sspmat_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. ! p - type(mld_s_interlev_prec_type), input/output. ! The one-level preconditioner data structure containing the local ! part of the base preconditioner to be built as well as the ! aggregate matrices. ! info - integer, output. ! Error code. ! subroutine mld_saggrmat_smth_asb(a,desc_a,p,info) use psb_base_mod use mld_inner_mod, mld_protect_name => mld_saggrmat_smth_asb #ifdef MPI_MOD use mpi #endif implicit none #ifdef MPI_H include 'mpif.h' #endif ! Arguments type(psb_sspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a type(mld_s_interlev_prec_type), intent(inout), target :: p integer, intent(out) :: info ! Local variables type(psb_sspmat_type) :: b integer, allocatable :: nzbr(:), idisp(:) integer :: nrow, nglob, ncol, ntaggr, nzac, ip, ndx,& & naggr, nzl,naggrm1,naggrp1, i, j, k integer ::ictxt,np,me, err_act, icomm character(len=20) :: name type(psb_sspmat_type) :: am1,am2 type(psb_sspmat_type) :: am3,am4 real(psb_spk_), allocatable :: adiag(:) logical :: ml_global_nmb integer :: debug_level, debug_unit integer, parameter :: ncmax=16 real(psb_spk_) :: omega, anorm, tmp, dg name='mld_aggrmat_smth_asb' if(psb_get_errstatus().ne.0) return info=0 call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ictxt = psb_cd_get_context(desc_a) icomm = psb_cd_get_mpic(desc_a) ictxt = psb_cd_get_context(desc_a) call psb_info(ictxt, me, np) call psb_nullify_sp(b) call psb_nullify_sp(am3) call psb_nullify_sp(am4) call psb_nullify_sp(am1) call psb_nullify_sp(am2) nglob = psb_cd_get_global_rows(desc_a) nrow = psb_cd_get_local_rows(desc_a) ncol = psb_cd_get_local_cols(desc_a) naggr = p%nlaggr(me+1) ntaggr = sum(p%nlaggr) allocate(nzbr(np), idisp(np),stat=info) if (info /= 0) then info=4025 call psb_errpush(info,name,i_err=(/2*np,0,0,0,0/),& & a_err='integer') goto 9999 end if naggrm1 = sum(p%nlaggr(1:me)) naggrp1 = sum(p%nlaggr(1:me+1)) ml_global_nmb = ( (p%iprcparm(mld_aggr_kind_) == mld_smooth_prol_).or.& & ( (p%iprcparm(mld_aggr_kind_) == mld_biz_prol_).and.& & (p%iprcparm(mld_coarse_mat_) == mld_repl_mat_)) ) if (ml_global_nmb) then p%mlia(1:nrow) = p%mlia(1:nrow) + naggrm1 call psb_halo(p%mlia,desc_a,info) if (info /= 0) then call psb_errpush(4010,name,a_err='psb_halo') goto 9999 end if end if ! naggr: number of local aggregates ! nrow: local rows. ! allocate(adiag(nrow),stat=info) if (info /= 0) then info=4025 call psb_errpush(info,name,i_err=(/nrow,0,0,0,0/),& & a_err='real(psb_spk_)') goto 9999 end if ! Get diagonal D call psb_sp_getdiag(a,adiag,info) if(info /= 0) then call psb_errpush(4010,name,a_err='sp_getdiag') goto 9999 end if do i=1,size(adiag) if (adiag(i) /= szero) then adiag(i) = sone / adiag(i) else adiag(i) = sone end if end do ! 1. Allocate Ptilde in sparse matrix form am4%fida='COO' am4%m=ncol if (ml_global_nmb) then am4%k=ntaggr call psb_sp_all(ncol,ntaggr,am4,ncol,info) else am4%k=naggr call psb_sp_all(ncol,naggr,am4,ncol,info) endif if (info /= 0) then call psb_errpush(4010,name,a_err='spall') goto 9999 end if if (ml_global_nmb) then do i=1,ncol am4%aspk(i) = sone am4%ia1(i) = i am4%ia2(i) = p%mlia(i) end do am4%infoa(psb_nnz_) = ncol else do i=1,nrow am4%aspk(i) = sone am4%ia1(i) = i am4%ia2(i) = p%mlia(i) end do am4%infoa(psb_nnz_) = nrow endif call psb_spcnv(am4,info,afmt='csr',dupl=psb_dupl_add_) if (info==0) call psb_spcnv(a,am3,info,afmt='csr',dupl=psb_dupl_add_) if (info /= 0) then call psb_errpush(4010,name,a_err='spcnv') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & ' Initial copies done.' ! ! WARNING: the cycles below assume that AM3 does have ! its diagonal elements stored explicitly!!! ! Should we switch to something safer? ! call psb_sp_scal(am3,adiag,info) if (info /= 0) goto 9999 if (p%iprcparm(mld_aggr_omega_alg_) == mld_eig_est_) then if (p%iprcparm(mld_aggr_eig_) == mld_max_norm_) then if (p%iprcparm(mld_aggr_kind_) == mld_biz_prol_) then ! ! This only works with CSR. ! if (psb_toupper(am3%fida)=='CSR') then anorm = szero dg = sone do i=1,am3%m tmp = szero do j=am3%ia2(i),am3%ia2(i+1)-1 if (am3%ia1(j) <= am3%m) then tmp = tmp + abs(am3%aspk(j)) endif if (am3%ia1(j) == i ) then dg = abs(am3%aspk(j)) end if end do anorm = max(anorm,tmp/dg) enddo call psb_amx(ictxt,anorm) else info = 4001 call psb_errpush(info,name,a_err='this section only CSR') goto 9999 endif else anorm = psb_spnrmi(am3,desc_a,info) endif if (info /= 0) then call psb_errpush(4001,name,a_err='Invalid AM3 storage format') goto 9999 end if omega = 4.d0/(3.d0*anorm) p%rprcparm(mld_aggr_omega_val_) = omega else info = 4001 call psb_errpush(info,name,a_err='invalid mld_aggr_eig_') goto 9999 end if else if (p%iprcparm(mld_aggr_omega_alg_) == mld_user_choice_) then omega = p%rprcparm(mld_aggr_omega_val_) else if (p%iprcparm(mld_aggr_omega_alg_) /= mld_user_choice_) then info = 4001 call psb_errpush(info,name,a_err='invalid mld_aggr_omega_alg_') goto 9999 end if if (psb_toupper(am3%fida)=='CSR') then do i=1,am3%m do j=am3%ia2(i),am3%ia2(i+1)-1 if (am3%ia1(j) == i) then am3%aspk(j) = sone - omega*am3%aspk(j) else am3%aspk(j) = - omega*am3%aspk(j) end if end do end do else call psb_errpush(4001,name,a_err='Invalid AM3 storage format') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done gather, going for SYMBMM 1' ! ! Symbmm90 does the allocation for its result. ! ! am1 = (i-wDA)Ptilde ! Doing it this way means to consider diag(Ai) ! ! call psb_symbmm(am3,am4,am1,info) if(info /= 0) then call psb_errpush(4010,name,a_err='symbmm 1') goto 9999 end if call psb_numbmm(am3,am4,am1) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 1' call psb_sp_free(am4,info) if(info /= 0) then call psb_errpush(4010,name,a_err='sp_free') goto 9999 end if if (ml_global_nmb) then ! ! Now we have to gather the halo of am1, and add it to itself ! to multiply it by A, ! call psb_sphalo(am1,desc_a,am4,info,& & colcnv=.false.,rowscale=.true.) if (info == 0) call psb_rwextd(ncol,am1,info,b=am4) if (info == 0) call psb_sp_free(am4,info) else call psb_rwextd(ncol,am1,info) endif if(info /= 0) then call psb_errpush(4001,name,a_err='Halo of am1') goto 9999 end if call psb_symbmm(a,am1,am3,info) if(info /= 0) then call psb_errpush(4010,name,a_err='symbmm 2') goto 9999 end if call psb_numbmm(a,am1,am3) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 2' if (p%iprcparm(mld_aggr_kind_) == mld_smooth_prol_) then call psb_transp(am1,am2,fmt='COO') nzl = am2%infoa(psb_nnz_) i=0 ! ! Now we have to fix this. The only rows of B that are correct ! are those corresponding to "local" aggregates, i.e. indices in p%mlia(:) ! do k=1, nzl if ((naggrm1 < am2%ia1(k)) .and.(am2%ia1(k) <= naggrp1)) then i = i+1 am2%aspk(i) = am2%aspk(k) am2%ia1(i) = am2%ia1(k) am2%ia2(i) = am2%ia2(k) end if end do am2%infoa(psb_nnz_) = i call psb_spcnv(am2,info,afmt='csr',dupl=psb_dupl_add_) if (info /=0) then call psb_errpush(4010,name,a_err='spcnv am2') goto 9999 end if else call psb_transp(am1,am2) endif if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'starting sphalo/ rwxtd' if (p%iprcparm(mld_aggr_kind_) == mld_smooth_prol_) then ! am2 = ((i-wDA)Ptilde)^T call psb_sphalo(am3,desc_a,am4,info,& & colcnv=.false.,rowscale=.true.) if (info == 0) call psb_rwextd(ncol,am3,info,b=am4) if (info == 0) call psb_sp_free(am4,info) else if (p%iprcparm(mld_aggr_kind_) == mld_biz_prol_) then call psb_rwextd(ncol,am3,info) endif if(info /= 0) then call psb_errpush(4001,name,a_err='Extend am3') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'starting symbmm 3' call psb_symbmm(am2,am3,b,info) if (info == 0) call psb_numbmm(am2,am3,b) if (info == 0) call psb_sp_free(am3,info) if (info == 0) call psb_spcnv(b,info,afmt='coo',dupl=psb_dupl_add_) if (info /= 0) then call psb_errpush(4001,name,a_err='Build b = am2 x am3') goto 9999 end if select case(p%iprcparm(mld_aggr_kind_)) case(mld_smooth_prol_) select case(p%iprcparm(mld_coarse_mat_)) case(mld_distr_mat_) call psb_sp_clone(b,p%ac,info) nzac = p%ac%infoa(psb_nnz_) nzl = p%ac%infoa(psb_nnz_) if (info == 0) call psb_cdall(ictxt,p%desc_ac,info,nl=p%nlaggr(me+1)) if (info == 0) call psb_cdins(nzl,p%ac%ia1,p%ac%ia2,p%desc_ac,info) if (info == 0) call psb_cdasb(p%desc_ac,info) if (info == 0) call psb_glob_to_loc(p%ac%ia1(1:nzl),p%desc_ac,info,iact='I') if (info == 0) call psb_glob_to_loc(p%ac%ia2(1:nzl),p%desc_ac,info,iact='I') if (info /= 0) then call psb_errpush(4001,name,a_err='Creating p%desc_ac and converting ac') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Assembld aux descr. distr.' p%ac%m=psb_cd_get_local_rows(p%desc_ac) p%ac%k=psb_cd_get_local_cols(p%desc_ac) p%ac%fida='COO' p%ac%descra='GUN' call psb_sp_free(b,info) if (info == 0) deallocate(nzbr,idisp,stat=info) if (info /= 0) then call psb_errpush(4010,name,a_err='psb_sp_free') goto 9999 end if if (np>1) then nzl = psb_sp_get_nnzeros(am1) call psb_glob_to_loc(am1%ia1(1:nzl),p%desc_ac,info,'I') if(info /= 0) then call psb_errpush(4010,name,a_err='psb_glob_to_loc') goto 9999 end if endif am1%k=psb_cd_get_local_cols(p%desc_ac) if (np>1) then call psb_spcnv(am2,info,afmt='coo',dupl=psb_dupl_add_) nzl = am2%infoa(psb_nnz_) if (info == 0) call psb_glob_to_loc(am2%ia1(1:nzl),p%desc_ac,info,'I') if (info == 0) call psb_spcnv(am2,info,afmt='csr',dupl=psb_dupl_add_) if(info /= 0) then call psb_errpush(4001,name,a_err='Converting am2 to local') goto 9999 end if end if am2%m=psb_cd_get_local_cols(p%desc_ac) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done ac ' case(mld_repl_mat_) ! ! call psb_cdall(ictxt,p%desc_ac,info,mg=ntaggr,repl=.true.) nzbr(:) = 0 nzbr(me+1) = b%infoa(psb_nnz_) call psb_sum(ictxt,nzbr(1:np)) nzac = sum(nzbr) if (info == 0) call psb_sp_all(ntaggr,ntaggr,p%ac,nzac,info) if (info /= 0) goto 9999 do ip=1,np idisp(ip) = sum(nzbr(1:ip-1)) enddo ndx = nzbr(me+1) call mpi_allgatherv(b%aspk,ndx,mpi_real,p%ac%aspk,nzbr,idisp,& & mpi_real,icomm,info) if (info == 0) call mpi_allgatherv(b%ia1,ndx,mpi_integer,p%ac%ia1,nzbr,idisp,& & mpi_integer,icomm,info) if (info == 0) call mpi_allgatherv(b%ia2,ndx,mpi_integer,p%ac%ia2,nzbr,idisp,& & mpi_integer,icomm,info) if (info /= 0) then call psb_errpush(4001,name,a_err=' from mpi_allgatherv') goto 9999 end if p%ac%m = ntaggr p%ac%k = ntaggr p%ac%infoa(psb_nnz_) = nzac p%ac%fida='COO' p%ac%descra='GUN' call psb_spcnv(p%ac,info,afmt='coo',dupl=psb_dupl_add_) if(info /= 0) goto 9999 call psb_sp_free(b,info) if(info /= 0) goto 9999 deallocate(nzbr,idisp,stat=info) if (info /= 0) then info = 4000 call psb_errpush(info,name) goto 9999 end if case default info = 4001 call psb_errpush(info,name,a_err='invalid mld_coarse_mat_') goto 9999 end select case(mld_biz_prol_) select case(p%iprcparm(mld_coarse_mat_)) case(mld_distr_mat_) call psb_sp_clone(b,p%ac,info) if (info == 0) call psb_cdall(ictxt,p%desc_ac,info,nl=naggr) if (info == 0) call psb_cdasb(p%desc_ac,info) if (info == 0) call psb_sp_free(b,info) if (info /= 0) then call psb_errpush(4010,name,a_err='Build desc_ac, ac') goto 9999 end if case(mld_repl_mat_) ! ! call psb_cdall(ictxt,p%desc_ac,info,mg=ntaggr,repl=.true.) if(info /= 0) then call psb_errpush(4010,name,a_err='psb_cdall') goto 9999 end if nzbr(:) = 0 nzbr(me+1) = b%infoa(psb_nnz_) call psb_sum(ictxt,nzbr(1:np)) nzac = sum(nzbr) call psb_sp_all(ntaggr,ntaggr,p%ac,nzac,info) if(info /= 0) then call psb_errpush(4010,name,a_err='psb_sp_all') goto 9999 end if do ip=1,np idisp(ip) = sum(nzbr(1:ip-1)) enddo ndx = nzbr(me+1) call mpi_allgatherv(b%aspk,ndx,mpi_real,p%ac%aspk,nzbr,idisp,& & mpi_real,icomm,info) if (info == 0) call mpi_allgatherv(b%ia1,ndx,mpi_integer,p%ac%ia1,nzbr,idisp,& & mpi_integer,icomm,info) if (info == 0) call mpi_allgatherv(b%ia2,ndx,mpi_integer,p%ac%ia2,nzbr,idisp,& & mpi_integer,icomm,info) if (info /= 0) then call psb_errpush(4001,name,a_err=' from mpi_allgatherv') goto 9999 end if p%ac%m = ntaggr p%ac%k = ntaggr p%ac%infoa(psb_nnz_) = nzac p%ac%fida='COO' p%ac%descra='GUN' call psb_spcnv(p%ac,info,afmt='coo',dupl=psb_dupl_add_) if(info /= 0) then call psb_errpush(4010,name,a_err='spcnv') goto 9999 end if call psb_sp_free(b,info) if(info /= 0) then call psb_errpush(4010,name,a_err='psb_sp_free') goto 9999 end if case default info = 4001 call psb_errpush(info,name,a_err='invalid mld_coarse_mat_') goto 9999 end select deallocate(nzbr,idisp,stat=info) if (info /= 0) then info = 4000 call psb_errpush(info,name) goto 9999 end if case default info = 4001 call psb_errpush(info,name,a_err='invalid mld_smooth_prol_') goto 9999 end select call psb_spcnv(p%ac,info,afmt='csr',dupl=psb_dupl_add_) if(info /= 0) then call psb_errpush(4010,name,a_err='spcnv') goto 9999 end if ! ! Copy the prolongation/restriction matrices into the descriptor map. ! am2 => PR^T i.e. restriction operator ! am1 => PR i.e. prolongation operator ! p%map_desc = psb_linear_map(psb_map_aggr_,desc_a,& & p%desc_ac,am2,am1) if (info == 0) call psb_sp_free(am1,info) if (info == 0) call psb_sp_free(am2,info) if(info /= 0) then call psb_errpush(4010,name,a_err='sp_Free') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done smooth_aggregate ' call psb_erractionrestore(err_act) return 9999 continue call psb_errpush(info,name) call psb_erractionrestore(err_act) if (err_act.eq.psb_act_abort_) then call psb_error() return end if return end subroutine mld_saggrmat_smth_asb