!!$ !!$ !!$ MLD2P4 version 2.1 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 3.4) !!$ !!$ (C) Copyright 2008, 2010, 2012, 2015, 2017 !!$ !!$ Salvatore Filippone Cranfield University !!$ Ambra Abdullahi Hassan 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_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 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_sprecinit and mld_zprecset. ! ! 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_sprecinit and mld_zprecset. ! On output from this routine the entries of AC, op_prol, op_restr ! are still in "global numbering" mode; this is fixed in the calling routine ! mld_s_lev_aggrmat_asb. ! ! 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_onelev_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. ! parms - type(mld_sml_parms), input ! Parameters controlling the choice of algorithm ! ac - type(psb_sspmat_type), output ! The coarse matrix on output ! ! ilaggr - integer, dimension(:), input ! 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. Note that the indices ! are assumed to be shifted so as to make sure the ranges on ! the various processes do not overlap. ! nlaggr - integer, dimension(:) input ! nlaggr(i) contains the aggregates held by process i. ! op_prol - type(psb_sspmat_type), input/output ! The tentative prolongator on input, the computed prolongator on output ! ! op_restr - type(psb_sspmat_type), output ! The restrictor operator; normally, it is the transpose of the prolongator. ! ! info - integer, output. ! Error code. ! subroutine mld_saggrmat_smth_asb(a,desc_a,ilaggr,nlaggr,parms,ac,op_prol,op_restr,info) use psb_base_mod use mld_s_inner_mod, mld_protect_name => mld_saggrmat_smth_asb implicit none ! Arguments type(psb_sspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_), intent(inout) :: ilaggr(:), nlaggr(:) type(mld_sml_parms), intent(inout) :: parms type(psb_sspmat_type), intent(inout) :: op_prol type(psb_sspmat_type), intent(out) :: ac,op_restr integer(psb_ipk_), intent(out) :: info ! Local variables integer(psb_ipk_) :: nrow, nglob, ncol, ntaggr, ip, ndx,& & naggr, nzl,naggrm1,naggrp1, i, j, k, jd, icolF, nrw, err_act integer(psb_ipk_) ::ictxt, np, me character(len=20) :: name type(psb_sspmat_type) :: am3, am4, tmp_prol type(psb_s_coo_sparse_mat) :: tmpcoo type(psb_s_csr_sparse_mat) :: acsr1, acsr2, acsr3, acsrf, ptilde real(psb_spk_), allocatable :: adiag(:) integer(psb_ipk_) :: ierr(5) logical :: filter_mat integer(psb_ipk_) :: debug_level, debug_unit integer(psb_ipk_), parameter :: ncmax=16 real(psb_spk_) :: anorm, omega, 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() 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 = parms%aggr_thresh naggr = nlaggr(me+1) ntaggr = sum(nlaggr) naggrm1 = sum(nlaggr(1:me)) naggrp1 = sum(nlaggr(1:me+1)) filter_mat = (parms%aggr_filter == mld_filter_mat_) ! ! naggr: number of local aggregates ! nrow: local rows. ! ! Get the diagonal D adiag = a%get_diag(info) if (info == psb_success_) & & call psb_realloc(ncol,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 call op_prol%mv_to(tmpcoo) call ptilde%mv_from_coo(tmpcoo,info) if (info == psb_success_) call a%cscnv(acsr3,info,dupl=psb_dupl_add_) if (info /= psb_success_) goto 9999 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 acsr3%cp_to_fmt(acsrf,info) do i=1,nrow tmp = szero 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)=szero 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%clean_zeros(info) 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 if (filter_mat) call acsrf%scal(adiag,info) if (info == psb_success_) call acsr3%scal(adiag,info) if (info /= psb_success_) goto 9999 if (parms%aggr_omega_alg == mld_eig_est_) then if (parms%aggr_eig == mld_max_norm_) then anorm = acsr3%spnmi() omega = 4.d0/(3.d0*anorm) 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 (parms%aggr_omega_alg == mld_user_choice_) then omega = parms%aggr_omega_val else if (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) = sone - 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 SPSPMM 1' ! ! ! acsrm1 = (I-w*D*Af)Ptilde ! Doing it this way means to consider diag(Af_i) ! ! call psb_spspmm(acsrf,ptilde,acsr1,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spspmm 1') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done SPSPMM 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) = sone - 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 SPSPMM 1' ! ! acsrm1 = (I-w*D*A)Ptilde ! Doing it this way means to consider diag(A_i) ! ! call psb_spspmm(acsr3,ptilde,acsr1,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spspmm 1') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done SPSPMM 1' end if call ptilde%free() call acsr1%set_dupl(psb_dupl_add_) call op_prol%cp_from(acsr1) call tmp_prol%mv_from(acsr1) ! ! Now we have to gather the halo of tmp_prol, and add it to itself ! to multiply it by A, ! call psb_sphalo(tmp_prol,desc_a,am4,info,& & colcnv=.false.,rowscale=.true.) if (info == psb_success_) call psb_rwextd(ncol,tmp_prol,info,b=am4) if (info == psb_success_) call am4%free() if(info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Halo of tmp_prol') goto 9999 end if call psb_spspmm(a,tmp_prol,am3,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spspmm 2') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done SPSPMM 2',parms%aggr_kind, mld_smooth_prol_ call tmp_prol%cp_to(tmpcoo) call tmpcoo%transp() nzl = tmpcoo%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 < tmpcoo%ia(k)) .and.(tmpcoo%ia(k) <= naggrp1)) then i = i+1 tmpcoo%val(i) = tmpcoo%val(k) tmpcoo%ia(i) = tmpcoo%ia(k) tmpcoo%ja(i) = tmpcoo%ja(k) end if end do call tmpcoo%set_nzeros(i) ! call tmpcoo%trim() call op_restr%mv_from(tmpcoo) call op_restr%cscnv(info,type='csr',dupl=psb_dupl_add_) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spcnv op_restr') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'starting sphalo/ rwxtd' ! op_restr = ((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() 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 spspmm 3' call psb_spspmm(op_restr,am3,ac,info) if (info == psb_success_) call am3%free() if (info == psb_success_) call ac%cscnv(info,type='csr',dupl=psb_dupl_add_) if (info /= psb_success_) then call psb_errpush(psb_err_internal_error_,name,a_err='Build ac = op_restr x am3') 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_error_handler(err_act) return end subroutine mld_saggrmat_smth_asb