!!$ !!$ !!$ 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. 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File mld_ssub_solve.f90 ! ! Subroutine: mld_ssub_solve ! Version: real ! ! This routine computes ! ! Y = beta*Y + alpha*op(K^(-1))*X, ! ! where ! - K is a factored matrix, as specified below, ! - op(K^(-1)) is K^(-1) or its transpose, according to the value of the ! argument trans, ! - X and Y are vectors, ! - alpha and beta are scalars. ! ! Depending on K, alpha and beta (and on the communication descriptor desc_data ! - see the arguments below), the above computation may correspond to one of ! the following tasks: ! ! 1. approximate solution of a linear system ! ! A*Y = X, ! ! by using the L and U factors computed with an ILU (incomplete LU) factorization ! of A. In this case K = L*U ~ A, alpha = 1 and beta = 0. The factors L and U ! (and the matrix A) are either distributed and block-diagonal or replicated. ! ! 2. Solution of a linear system ! ! A*Y = X, ! ! by using the L and U factors computed with a LU factorization of A. In this ! case K = L*U = A, alpha = 1 and beta = 0. The LU factorization is performed ! by one of the following auxiliary pakages: ! a. UMFPACK, ! b. SuperLU, ! c. SuperLU_Dist. ! In the cases a. and b., the factors L and U (and the matrix A) are either ! distributed and block diagonal) or replicated; in the case c., L, U (and A) ! are distributed. ! ! This routine is used by mld_ssub_aply, to apply a 'base' block-Jacobi or ! Additive Schwarz (AS) preconditioner at any level of a multilevel preconditioner, ! or a block-Jacobi or LU or ILU solver at the coarsest level of a multilevel ! preconditioner. ! ! ! Arguments: ! ! alpha - real(psb_spk_), input. ! The scalar alpha. ! prec - type(mld_sbaseprec_type), input. ! The 'base preconditioner' data structure containing the local ! part of the L and U factors of the matrix A. ! x - real(psb_spk_), dimension(:), input. ! The local part of the vector X. ! beta - real(psb_spk_), input. ! The scalar beta. ! y - real(psb_spk_), dimension(:), input/output. ! The local part of the vector Y. ! desc_data - type(psb_desc_type), input. ! The communication descriptor associated to the matrix to be ! preconditioned or 'inverted'. ! trans - character(len=1), input. ! If trans='N','n' then op(K^(-1)) = K^(-1); ! if trans='T','t' then op(K^(-1)) = K^(-T) (transpose of K^(-1)). ! If prec%iprcparm(mld_smoother_sweeps_) > 1, the value of trans provided ! in input is ignored. ! work - real(psb_spk_), dimension (:), target. ! Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data). ! info - integer, output. ! Error code. ! subroutine mld_ssub_solve(alpha,prec,x,beta,y,desc_data,trans,work,info) use psb_base_mod use mld_inner_mod, mld_protect_name => mld_ssub_solve implicit none ! Arguments type(psb_desc_type), intent(in) :: desc_data type(mld_sbaseprc_type), intent(in) :: prec real(psb_spk_),intent(in) :: x(:) real(psb_spk_),intent(inout) :: y(:) real(psb_spk_),intent(in) :: alpha,beta character(len=1),intent(in) :: trans real(psb_spk_),target, intent(inout) :: work(:) integer, intent(out) :: info ! Local variables integer :: n_row,n_col real(psb_spk_), pointer :: ww(:), aux(:), tx(:),ty(:) integer :: ictxt,np,me,i, err_act character(len=20) :: name character :: trans_ interface subroutine mld_sumf_solve(flag,m,x,b,n,ptr,info) use psb_base_mod integer, intent(in) :: flag,m,n,ptr integer, intent(out) :: info real(psb_spk_), intent(in) :: b(*) real(psb_spk_), intent(inout) :: x(*) end subroutine mld_sumf_solve end interface name='mld_ssub_solve' info = 0 call psb_erractionsave(err_act) ictxt=psb_cd_get_context(desc_data) call psb_info(ictxt, me, np) trans_ = psb_toupper(trans) select case(trans_) case('N') case('T','C') case default call psb_errpush(40,name) goto 9999 end select n_row = psb_cd_get_local_rows(desc_data) n_col = psb_cd_get_local_cols(desc_data) if (n_col <= size(work)) then ww => work(1:n_col) if ((4*n_col+n_col) <= size(work)) then aux => work(n_col+1:) else allocate(aux(4*n_col),stat=info) if (info /= 0) then info=4025 call psb_errpush(info,name,i_err=(/4*n_col,0,0,0,0/),& & a_err='real(psb_spk_)') goto 9999 end if endif else allocate(ww(n_col),aux(4*n_col),stat=info) if (info /= 0) then info=4025 call psb_errpush(info,name,i_err=(/5*n_col,0,0,0,0/),& & a_err='real(psb_spk_)') goto 9999 end if endif select case(prec%iprcparm(mld_sub_solve_)) case(mld_ilu_n_,mld_milu_n_,mld_ilu_t_) ! ! Apply a block-Jacobi preconditioner with ILU(k)/MILU(k)/ILU(k,t) ! factorization of the blocks (distributed matrix) or approximately ! solve a system through ILU(k)/MILU(k)/ILU(k,t) (replicated matrix). ! select case(trans_) case('N') call psb_spsm(sone,prec%av(mld_l_pr_),x,szero,ww,desc_data,info,& & trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux) if (info == 0) call psb_spsm(alpha,prec%av(mld_u_pr_),ww,beta,y,desc_data,info,& & trans=trans_,unit='U',choice=psb_none_, work=aux) case('T','C') call psb_spsm(sone,prec%av(mld_u_pr_),x,szero,ww,desc_data,info,& & trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux) if (info == 0) call psb_spsm(alpha,prec%av(mld_l_pr_),ww,beta,y,desc_data,info,& & trans=trans_,unit='U',choice=psb_none_,work=aux) case default call psb_errpush(4001,name,a_err='Invalid TRANS in ILU subsolve') goto 9999 end select case(mld_slu_) ! ! Apply a block-Jacobi preconditioner with LU factorization of the ! blocks (distributed matrix) or approximately solve a local linear ! system through LU (replicated matrix). The SuperLU package is used ! to apply the LU factorization in both cases. ! ww(1:n_row) = x(1:n_row) select case(trans_) case('N') call mld_sslu_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info) case('T','C') call mld_sslu_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info) case default call psb_errpush(4001,name,a_err='Invalid TRANS in SLU subsolve') goto 9999 end select if (info ==0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info) case(mld_sludist_) ! ! Solve a distributed linear system with the LU factorization. ! The SuperLU_DIST package is used. ! ww(1:n_row) = x(1:n_row) select case(trans_) case('N') call mld_ssludist_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info) case('T','C') call mld_ssludist_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info) case default call psb_errpush(4001,name,a_err='Invalid TRANS in SLUDist subsolve') goto 9999 end select if (info == 0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info) case (mld_umf_) ! ! Apply a block-Jacobi preconditioner with LU factorization of the ! blocks (distributed matrix) or approximately solve a local linear ! system through LU (replicated matrix). The UMFPACK package is used ! to apply the LU factorization in both cases. ! select case(trans_) case('N') call mld_sumf_solve(0,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info) case('T','C') call mld_sumf_solve(1,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info) case default call psb_errpush(4001,name,a_err='Invalid TRANS in UMF subsolve') goto 9999 end select if (info == 0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info) case default call psb_errpush(4001,name,a_err='Invalid mld_sub_solve_') goto 9999 end select if (info /= 0) then call psb_errpush(4001,name,a_err='Error in subsolve') goto 9999 endif if (n_col <= size(work)) then if ((4*n_col+n_col) <= size(work)) then else deallocate(aux) endif else deallocate(ww,aux) endif 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_ssub_solve