!!$ !!$ !!$ MLD2P4 version 2.0 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 3.0) !!$ !!$ (C) Copyright 2008,2009,2010 !!$ !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse !!$ 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. 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File: mld_daggrmat_smth_asb.F90 ! ! Subroutine: mld_daggrmat_smth_asb ! Version: real ! ! This routine builds a coarse-level matrix A_C from a fine-level matrix A ! by using the 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%parms%aggr_omega_alg, specified by the user ! through mld_dprecinit and mld_dprecset. ! ! 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%parms%coarse_mat, ! specified by the user through mld_dprecinit and mld_dprecset. ! ! 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_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. ! p - type(mld_donelev_type), input/output. ! The 'one-level' data structure that will contain the local ! part of the matrix to be built as well as the information ! concerning the prolongator and its transpose. ! 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. ! nlaggr - integer, dimension(:), allocatable. ! nlaggr(i) contains the aggregates held by process i. ! info - integer, output. ! Error code. ! subroutine mld_daggrmat_smth_asb(a,desc_a,ilaggr,nlaggr,p,info) use psb_base_mod use mld_d_inner_mod, mld_protect_name => mld_daggrmat_smth_asb #ifdef MPI_MOD use mpi #endif implicit none #ifdef MPI_H include 'mpif.h' #endif ! Arguments type(psb_dspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a integer, intent(inout) :: ilaggr(:), nlaggr(:) type(mld_donelev_type), intent(inout), target :: p integer, intent(out) :: info ! Local variables type(psb_dspmat_type) :: b integer, allocatable :: nzbr(:), idisp(:) integer :: nrow, nglob, ncol, ntaggr, nzac, ip, ndx,& & naggr, nzl,naggrm1,naggrp1, i, j, k, jd, icolF, nrw integer ::ictxt,np,me, err_act, icomm character(len=20) :: name type(psb_dspmat_type) :: am1,am2, am3, am4 type(psb_d_coo_sparse_mat) :: acoo, acoof, bcoo type(psb_d_csr_sparse_mat) :: acsr1, acsr2, acsr3, acsrf, ptilde real(psb_dpk_), allocatable :: adiag(:) logical :: ml_global_nmb, filter_mat integer :: debug_level, debug_unit integer, parameter :: ncmax=16 real(psb_dpk_) :: omega, anorm, tmp, dg, theta name='mld_aggrmat_smth_asb' if(psb_get_errstatus().ne.0) return info=psb_success_ call psb_erractionsave(err_act) debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ictxt = desc_a%get_context() icomm = desc_a%get_mpic() ictxt = desc_a%get_context() call psb_info(ictxt, me, np) nglob = desc_a%get_global_rows() nrow = desc_a%get_local_rows() ncol = desc_a%get_local_cols() theta = p%parms%aggr_thresh naggr = nlaggr(me+1) ntaggr = sum(nlaggr) allocate(nzbr(np), idisp(np),stat=info) if (info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/2*np,0,0,0,0/),& & a_err='integer') goto 9999 end if naggrm1 = sum(nlaggr(1:me)) naggrp1 = sum(nlaggr(1:me+1)) ml_global_nmb = ( (p%parms%aggr_kind == mld_smooth_prol_).or.& & ( (p%parms%aggr_kind == mld_biz_prol_).and.& & (p%parms%coarse_mat == mld_repl_mat_)) ) filter_mat = (p%parms%aggr_filter == mld_filter_mat_) if (ml_global_nmb) then ilaggr(1:nrow) = ilaggr(1:nrow) + naggrm1 call psb_halo(ilaggr,desc_a,info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_halo') goto 9999 end if end if ! naggr: number of local aggregates ! nrow: local rows. ! allocate(adiag(ncol),stat=info) if (info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/nrow,0,0,0,0/),& & a_err='real(psb_dpk_)') goto 9999 end if ! Get the diagonal D call a%get_diag(adiag,info) if (info == psb_success_) & & call psb_halo(adiag,desc_a,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='sp_getdiag') goto 9999 end if ! 1. Allocate Ptilde in sparse matrix form if (ml_global_nmb) then call acoo%allocate(ncol,ntaggr,ncol) do i=1,ncol acoo%val(i) = done acoo%ia(i) = i acoo%ja(i) = ilaggr(i) end do call acoo%set_nzeros(ncol) else call acoo%allocate(ncol,naggr,ncol) do i=1,nrow acoo%val(i) = done acoo%ia(i) = i acoo%ja(i) = ilaggr(i) end do call acoo%set_nzeros(nrow) endif call acoo%set_dupl(psb_dupl_add_) call ptilde%mv_from_coo(acoo,info) if (info == psb_success_) call a%cscnv(acsr3,info,dupl=psb_dupl_add_) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & ' Initial copies done.' if (filter_mat) then ! ! Build the filtered matrix Af from A ! if (info == psb_success_) call a%cscnv(acsrf,info,dupl=psb_dupl_add_) do i=1,nrow tmp = dzero jd = -1 do j=acsrf%irp(i),acsrf%irp(i+1)-1 if (acsrf%ja(j) == i) jd = j if (abs(acsrf%val(j)) < theta*sqrt(abs(adiag(i)*adiag(acsrf%ja(j))))) then tmp=tmp+acsrf%val(j) acsrf%val(j)=dzero endif enddo if (jd == -1) then write(0,*) 'Wrong input: we need the diagonal!!!!', i else acsrf%val(jd)=acsrf%val(jd)-tmp end if enddo ! Take out zeroed terms call acsrf%mv_to_coo(acoof,info) k = 0 do j=1,acoof%get_nzeros() if ((acoof%val(j) /= dzero) .or. (acoof%ia(j) == acoof%ja(j))) then k = k + 1 acoof%val(k) = acoof%val(j) acoof%ia(k) = acoof%ia(j) acoof%ja(k) = acoof%ja(j) end if end do call acoof%set_nzeros(k) call acoof%set_dupl(psb_dupl_add_) call acsrf%mv_from_coo(acoof,info) end if do i=1,size(adiag) if (adiag(i) /= dzero) then adiag(i) = done / adiag(i) else adiag(i) = done end if end do if (filter_mat) call acsrf%scal(adiag,info) if (info == psb_success_) call acsr3%scal(adiag,info) if (info /= psb_success_) goto 9999 if (p%parms%aggr_omega_alg == mld_eig_est_) then if (p%parms%aggr_eig == mld_max_norm_) then if (p%parms%aggr_kind == mld_biz_prol_) then ! ! This only works with CSR ! anorm = dzero dg = done nrw = acsr3%get_nrows() do i=1, nrw tmp = dzero do j=acsr3%irp(i),acsr3%irp(i+1)-1 if (acsr3%ja(j) <= nrw) then tmp = tmp + abs(acsr3%val(j)) endif if (acsr3%ja(j) == i ) then dg = abs(acsr3%val(j)) end if end do anorm = max(anorm,tmp/dg) enddo call psb_amx(ictxt,anorm) else anorm = acsr3%csnmi() endif if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Invalid AM3 storage format') goto 9999 end if omega = 4.d0/(3.d0*anorm) p%parms%aggr_omega_val = omega else info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invalid mld_aggr_eig_') goto 9999 end if else if (p%parms%aggr_omega_alg == mld_user_choice_) then omega = p%parms%aggr_omega_val else if (p%parms%aggr_omega_alg /= mld_user_choice_) then info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invalid mld_aggr_omega_alg_') goto 9999 end if if (filter_mat) then ! ! Build the smoothed prolongator using the filtered matrix ! do i=1,acsrf%get_nrows() do j=acsrf%irp(i),acsrf%irp(i+1)-1 if (acsrf%ja(j) == i) then acsrf%val(j) = done - omega*acsrf%val(j) else acsrf%val(j) = - omega*acsrf%val(j) end if end do end do 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. ! ! acsrm1 = (I-w*D*Af)Ptilde ! Doing it this way means to consider diag(Af_i) ! ! call psb_symbmm(acsrf,ptilde,acsr1,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='symbmm 1') goto 9999 end if call psb_numbmm(acsrf,ptilde,acsr1) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 1' else ! ! Build the smoothed prolongator using the original matrix ! do i=1,acsr3%get_nrows() do j=acsr3%irp(i),acsr3%irp(i+1)-1 if (acsr3%ja(j) == i) then acsr3%val(j) = done - omega*acsr3%val(j) else acsr3%val(j) = - omega*acsr3%val(j) end if end do end do 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. ! ! acsrm1 = (I-w*D*A)Ptilde ! Doing it this way means to consider diag(A_i) ! ! call psb_symbmm(acsr3,ptilde,acsr1,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='symbmm 1') goto 9999 end if call psb_numbmm(acsr3,ptilde,acsr1) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 1' end if call ptilde%free() call acsr1%set_dupl(psb_dupl_add_) call am1%mv_from(acsr1) 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 == psb_success_) call psb_rwextd(ncol,am1,info,b=am4) if (info == psb_success_) call am4%free() else call psb_rwextd(ncol,am1,info) endif if(info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Halo of am1') goto 9999 end if call psb_symbmm(a,am1,am3,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,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',p%parms%aggr_kind, mld_smooth_prol_ if (p%parms%aggr_kind == mld_smooth_prol_) then call am2%transp(am1) call am2%mv_to(acoo) nzl = acoo%get_nzeros() 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 ilaggr(:) ! do k=1, nzl if ((naggrm1 < acoo%ia(k)) .and.(acoo%ia(k) <= naggrp1)) then i = i+1 acoo%val(i) = acoo%val(k) acoo%ia(i) = acoo%ia(k) acoo%ja(i) = acoo%ja(k) end if end do call acoo%set_nzeros(i) call acoo%trim() call am2%mv_from(acoo) call am2%cscnv(info,type='csr',dupl=psb_dupl_add_) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spcnv am2') goto 9999 end if else call am2%transp(am1) endif if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'starting sphalo/ rwxtd' if (p%parms%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 == psb_success_) call psb_rwextd(ncol,am3,info,b=am4) if (info == psb_success_) call am4%free() else if (p%parms%aggr_kind == mld_biz_prol_) then call psb_rwextd(ncol,am3,info) endif if(info /= psb_success_) then call psb_errpush(psb_err_internal_error_,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 == psb_success_) call psb_numbmm(am2,am3,b) if (info == psb_success_) call am3%free() if (info == psb_success_) call b%cscnv(info,type='coo',dupl=psb_dupl_add_) if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Build b = am2 x am3') goto 9999 end if select case(p%parms%aggr_kind) case(mld_smooth_prol_) select case(p%parms%coarse_mat) case(mld_distr_mat_) nzac = b%get_nzeros() nzl = nzac call b%mv_to(bcoo) if (info == psb_success_) call psb_cdall(ictxt,p%desc_ac,info,nl=nlaggr(me+1)) if (info == psb_success_) call psb_cdins(nzl,bcoo%ia,bcoo%ja,p%desc_ac,info) if (info == psb_success_) call psb_cdasb(p%desc_ac,info) if (info == psb_success_) call psb_glob_to_loc(bcoo%ia(1:nzl),p%desc_ac,info,iact='I') if (info == psb_success_) call psb_glob_to_loc(bcoo%ja(1:nzl),p%desc_ac,info,iact='I') if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,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.' call p%ac%mv_from(bcoo) call p%ac%set_nrows(p%desc_ac%get_local_rows()) call p%ac%set_ncols(p%desc_ac%get_local_cols()) call p%ac%set_asb() if (info == psb_success_) deallocate(nzbr,idisp,stat=info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_sp_free') goto 9999 end if if (np>1) then call am1%mv_to(acsr1) nzl = acsr1%get_nzeros() call psb_glob_to_loc(acsr1%ja(1:nzl),p%desc_ac,info,'I') if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_glob_to_loc') goto 9999 end if call am1%mv_from(acsr1) endif call am1%set_ncols(p%desc_ac%get_local_cols()) if (np>1) then call am2%cscnv(info,type='coo',dupl=psb_dupl_add_) call am2%mv_to(acoo) nzl = acoo%get_nzeros() if (info == psb_success_) call psb_glob_to_loc(acoo%ia(1:nzl),p%desc_ac,info,'I') call acoo%set_dupl(psb_dupl_add_) if (info == psb_success_) call am2%mv_from(acoo) if (info == psb_success_) call am2%cscnv(info,type='csr') if(info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Converting am2 to local') goto 9999 end if end if call am2%set_nrows(p%desc_ac%get_local_cols()) 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.) if (info == psb_success_) call psb_cdasb(p%desc_ac,info) if (info == psb_success_) & & call psb_gather(p%ac,b,p%desc_ac,info,dupl=psb_dupl_add_,keeploc=.false.) if (info /= psb_success_) goto 9999 deallocate(nzbr,idisp,stat=info) if (info /= psb_success_) then info = psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 end if case default info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invalid mld_coarse_mat_') goto 9999 end select case(mld_biz_prol_) select case(p%parms%coarse_mat) case(mld_distr_mat_) call psb_move_alloc(b,p%ac,info) if (info == psb_success_) call psb_cdall(ictxt,p%desc_ac,info,nl=naggr) if (info == psb_success_) call psb_cdasb(p%desc_ac,info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,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 == psb_success_) call psb_cdasb(p%desc_ac,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_cdall') goto 9999 end if call psb_gather(p%ac,b,p%desc_ac,info,dupl=psb_dupl_add_,keeploc=.false.) if(info /= psb_success_) goto 9999 deallocate(nzbr,idisp,stat=info) if (info /= psb_success_) then info = psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 end if case default info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invalid mld_coarse_mat_') goto 9999 end select deallocate(nzbr,idisp,stat=info) if (info /= psb_success_) then info = psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 end if case default info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invalid mld_smooth_prol_') goto 9999 end select call p%ac%cscnv(info,type='csr',dupl=psb_dupl_add_) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,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 = psb_linmap(psb_map_aggr_,desc_a,& & p%desc_ac,am2,am1,ilaggr,nlaggr) if (info == psb_success_) call am1%free() if (info == psb_success_) call am2%free() if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,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_daggrmat_smth_asb