!!$ !!$ !!$ MLD2P4 version 1.1 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS version 2.3.1) !!$ !!$ (C) Copyright 2008,2009 !!$ !!$ 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. 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File: mld_zexample_ml.f90 ! ! This sample program solves a linear system by using BiCGStab coupled with ! one of the following multi-level preconditioner, as explained in Section 6.1 ! of the MLD2P4 User's and Reference Guide: ! - choice = 1, default multi-level Schwarz preconditioner (Sec. 6.1, Fig. 2) ! - choice = 2, hybrid three-level Schwarz preconditioner (Sec. 6.1, Fig. 3) ! - choice = 3, additive three-level Schwarz preconditioner (Sec. 6.1, Fig. 4) ! ! The matrix and the rhs are read from files (if an rhs is not available, the ! unit rhs is set). ! program mld_zexample_ml use psb_sparse_mod use mld_prec_mod use psb_krylov_mod use psb_util_mod use data_input implicit none ! input file parameters character(len=40) :: mtrx_file, rhs_file character(len=2) :: filefmt ! sparse matrices type(psb_zspmat_type) :: A, aux_A ! descriptor of sparse matrices type(psb_desc_type):: desc_A ! preconditioner type(mld_zprec_type) :: P ! right-hand side, solution and residual vectors complex(psb_dpk_), allocatable , save :: b(:), x(:), r(:), & & x_glob(:), r_glob(:) complex(psb_dpk_), allocatable, target :: aux_b(:,:) complex(psb_dpk_), pointer :: b_glob(:) ! solver and preconditioner parameters real(psb_dpk_) :: tol, err integer :: itmax, iter, istop integer :: nlev ! parallel environment parameters integer :: ictxt, iam, np ! other variables integer :: choice integer :: i,info,j,m_problem integer(psb_long_int_k_) :: amatsize, precsize, descsize integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=20) :: name integer, parameter :: iunit=12 ! initialize the parallel environment call psb_init(ictxt) call psb_info(ictxt,iam,np) if (iam < 0) then ! This should not happen, but just in case call psb_exit(ictxt) stop endif name='mld_zexample_ml' if(psb_get_errstatus() /= 0) goto 9999 info=psb_success_ call psb_set_errverbosity(2) ! get parameters call get_parms(ictxt,mtrx_file,rhs_file,filefmt,choice,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() ! read and assemble the matrix A and the right-hand side b ! using PSBLAS routines for sparse matrix / vector management if (iam == psb_root_) then select case(psb_toupper(filefmt)) case('MM') ! For Matrix Market we have an input file for the matrix ! and an (optional) second file for the RHS. call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) if (info == psb_success_) then if (rhs_file /= 'NONE') then call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) end if end if case ('HB') ! For Harwell-Boeing we have a single file which may or may not ! contain an RHS. call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) case default info = -1 write(0,*) 'Wrong choice for fileformat ', filefmt end select if (info /= psb_success_) then write(0,*) 'Error while reading input matrix ' call psb_abort(ictxt) end if m_problem = aux_a%m call psb_bcast(ictxt,m_problem) ! At this point aux_b may still be unallocated if (psb_size(aux_b,1) == m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') b_glob =>aux_b(:,1) else write(*,'("Generating an rhs...")') write(*,'(" ")') call psb_realloc(m_problem,1,aux_b,ircode) if (ircode /= 0) then call psb_errpush(psb_err_alloc_dealloc_,name) goto 9999 endif b_glob => aux_b(:,1) do i=1, m_problem b_glob(i) = 1.d0 enddo endif call psb_bcast(ictxt,b_glob(1:m_problem)) else call psb_bcast(ictxt,m_problem) call psb_realloc(m_problem,1,aux_b,ircode) if (ircode /= 0) then call psb_errpush(psb_err_alloc_dealloc_,name) goto 9999 endif b_glob =>aux_b(:,1) call psb_bcast(ictxt,b_glob(1:m_problem)) end if call psb_barrier(ictxt) if (iam == psb_root_) write(*,'("Partition type: block")') call psb_matdist(aux_A, A, ictxt, & & desc_A,b_glob,b,info, parts=part_block) t2 = psb_wtime() - t1 call psb_amx(ictxt, t2) if (iam == psb_root_) then write(*,'(" ")') write(*,'("Time to read and partition matrix : ",es12.5)')t2 write(*,'(" ")') end if select case(choice) case(1) ! initialize the default multi-level preconditioner, i.e. hybrid ! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks) ! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU ! on the blocks) as distributed coarse-level solver call mld_precinit(P,'ML',info) case(2) ! set a three-level hybrid Schwarz preconditioner, which uses ! block Jacobi (with ILU(0) on the blocks) as post-smoother, ! a coarsest matrix replicated on the processors, and the ! LU factorization from UMFPACK as coarse-level solver call mld_precinit(P,'ML',info,nlev=3) call mld_precset(P,mld_smoother_type_,'BJAC',info) call mld_precset(P,mld_coarse_mat_,'REPL',info) call mld_precset(P,mld_coarse_solve_,'UMF',info) case(3) ! set a three-level additive Schwarz preconditioner, which uses ! RAS (with overlap 1 and ILU(0) on the blocks) as pre- and ! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU ! on the blocks) as distributed coarsest-level solver call mld_precinit(P,'ML',info,nlev=3) call mld_precset(P,mld_ml_type_,'ADD',info) call mld_precset(P,mld_smoother_pos_,'TWOSIDE',info) call mld_precset(P,mld_coarse_sweeps_,5,info) end select ! build the preconditioner call psb_barrier(ictxt) t1 = psb_wtime() call mld_precbld(A,desc_A,P,info) tprec = psb_wtime()-t1 call psb_amx(ictxt, tprec) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_precbld') goto 9999 end if ! set the initial guess call psb_geall(x,desc_A,info) x(:) =0.0 call psb_geasb(x,desc_A,info) ! solve Ax=b with preconditioned BiCGSTAB call psb_barrier(ictxt) t1 = psb_wtime() call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info,itmax,iter,err,itrace=1,istop=2) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) call psb_geall(r,desc_A,info) r(:) =0.0 call psb_geasb(r,desc_A,info) call psb_geaxpby(zone,b,zzero,r,desc_A,info) call psb_spmm(-zone,A,x,zone,r,desc_A,info) call psb_genrm2s(resmx,r,desc_A,info) call psb_geamaxs(resmxp,r,desc_A,info) amatsize = psb_sizeof(A) descsize = psb_sizeof(desc_A) precsize = mld_sizeof(P) call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) call psb_sum(ictxt,precsize) call mld_precdescr(P,info) if (iam == psb_root_) then write(*,'(" ")') write(*,'("Matrix: ",A)')mtrx_file write(*,'("Computed solution on ",i8," processors")')np write(*,'("Iterations to convergence : ",i6)')iter write(*,'("Error estimate on exit : ",es12.5)')err write(*,'("Time to build prec. : ",es12.5)')tprec write(*,'("Time to solve system : ",es12.5)')t2 write(*,'("Time per iteration : ",es12.5)')t2/(iter) write(*,'("Total time : ",es12.5)')t2+tprec write(*,'("Residual 2-norm : ",es12.5)')resmx write(*,'("Residual inf-norm : ",es12.5)')resmxp write(*,'("Total memory occupation for A : ",i12)')amatsize write(*,'("Total memory occupation for DESC_A : ",i12)')descsize write(*,'("Total memory occupation for PREC : ",i12)')precsize end if allocate(x_glob(m_problem),r_glob(m_problem),stat=ierr) if (ierr /= 0) then write(0,*) 'allocation error: no data collection' else call psb_gather(x_glob,x,desc_A,info,root=psb_root_) call psb_gather(r_glob,r,desc_A,info,root=psb_root_) if (iam == psb_root_) then write(0,'(" ")') write(0,'("Saving x on file")') write(20,*) 'matrix: ',mtrx_file write(20,*) 'computed solution on ',np,' processors.' write(20,*) 'iterations to convergence: ',iter write(20,*) 'error estimate (infinity norm) on exit:', & & ' ||r||/(||a||||x||+||b||) = ',err write(20,*) 'max residual = ',resmx, resmxp write(20,'(a8,4(2x,a20))') 'I','X(I)','R(I)','B(I)' do i=1,m_problem write(20,998) i,x_glob(i),r_glob(i),b_glob(i) enddo end if end if 998 format(i8,4(2x,g20.14)) 993 format(i6,4(1x,e12.6)) ! deallocate the data structures call psb_gefree(b, desc_A,info) call psb_gefree(x, desc_A,info) call psb_spfree(A, desc_A,info) call mld_precfree(P,info) call psb_cdfree(desc_A,info) 9999 continue if(info /= psb_success_) then call psb_error(ictxt) end if call psb_exit(ictxt) stop contains ! ! get parameters from standard input ! subroutine get_parms(ictxt,mtrx,rhs,filefmt,choice,itmax,tol) use psb_sparse_mod implicit none integer :: ictxt, choice, itmax real(psb_dpk_) :: tol character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) if (iam == psb_root_) then ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) call read_data(filefmt,5) call read_data(choice,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,choice) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) end subroutine get_parms end program mld_zexample_ml