!!$ !!$ !!$ MLD2P4 !!$ MultiLevel Domain Decomposition Parallel Preconditioners Package !!$ based on PSBLAS (Parallel Sparse BLAS v.2.0) !!$ !!$ (C) Copyright 2007 Alfredo Buttari University of Rome Tor Vergata !!$ Pasqua D'Ambra ICAR-CNR, Naples !!$ Daniela di Serafino Second University of Naples !!$ Salvatore Filippone University of Rome Tor Vergata !!$ !!$ 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_zbjac_aply.f90 ! ! Subroutine: mld_zbjac_aply ! Version: complex ! ! This routine computes ! ! Y = beta*Y + alpha*op(K^(-1))*X, ! ! where ! - K is a suitable matrix, as specified below, ! - op(K^(-1)) is K^(-1) or its transpose, according to the value of trans, ! - X and Y are vectors, ! - alpha and beta are scalars. ! ! Depending on K, alpha, beta (and on the communication descriptor desc_data ! - see the arguments below), the above computation may correspond to one of ! the following tasks: ! ! 1. Application of a block-Jacobi preconditioner associated to a matrix A ! distributed among the processes. Here K is the preconditioner, op(K^(-1)) ! = K^(-1), alpha = 1 and beta = 0. ! ! 2. Application of block-Jacobi sweeps to compute an approximate solution of ! a linear system ! A*Y = X, ! ! distributed among the processes (note that a single block-Jacobi sweep, ! with null starting guess, corresponds to the application of a block-Jacobi ! preconditioner). Here K^(-1) denotes the iteration matrix of the ! block-Jacobi solver, op(K^(-1)) = K^(-1), alpha = 1 and beta = 0. ! ! 3. Solution, through the LU factorization, of a linear system ! ! A*Y = X, ! ! distributed among the processes. Here K = L*U = A, op(K^(-1)) = K^(-1), ! alpha = 1 and beta = 0. ! ! 4. (Approximate) solution, through the LU or incomplete LU factorization, of ! a linear system ! A*Y = X, ! ! replicated on the processes. Here K = L*U = A or K = L*U ~ A, op(K^(-1)) = ! K^(-1), alpha = 1 and beta = 0. ! ! The block-Jacobi preconditioner or solver and the L and U factors of the LU ! or ILU factorizations have been built by the routine mld_dbjac_bld and stored ! into the 'base preconditioner' data structure prec. See mld_dbjac_bld for more ! details. ! ! This routine is used by mld_dbaseprec_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. ! ! Inside mld_dbaseprec_aply, tasks 1, 3 and 4 may be selected if ! prec%iprcparm(smooth_sweeps_) = 1, while task 2 if prec%iprcparm(smooth_sweeps_) ! > 1. Furthermore, tasks 1, 2 and 3 may be performed if the matrix A is ! distributed among the processes (prec%iprcparm(mld_coarse_mat_) = mld_distr_mat_), ! while task 4 may be performed if A is replicated on the processes ! (prec%iprcparm(mld_coarse_mat_) = mld_repl_mat_). Note that the matrix A is ! distributed among the processes at each level of the multilevel preconditioner, ! except the coarsest one, where it may be either distributed or replicated on ! the processes. Furthermore, the tasks 2, 3 and 4 are performed only at the ! coarsest level. Note also that this routine manages implicitly the fact that ! the matrix is distributed or replicated, i.e. it does not make any explicit ! reference to the value of prec%iprcparm(mld_coarse_mat_). ! ! ! Arguments: ! ! alpha - complex(kind(0.d0)), input. ! The scalar alpha. ! prec - type(mld_zbaseprec_type), input. ! The 'base preconditioner' data structure containing the local ! part of the preconditioner or solver. ! x - complex(kind(0.d0)), dimension(:), input. ! The local part of the vector X. ! beta - complex(kind(0.d0)), input. ! The scalar beta. ! y - complex(kind(0.d0)), 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(smooth_sweeps_) > 1, the value of trans provided ! in input is ignored. ! work - complex(kind(0.d0)), dimension (:), target. ! Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data). ! info - integer, output. ! Error code. ! subroutine mld_zbjac_aply(alpha,prec,x,beta,y,desc_data,trans,work,info) use psb_base_mod use mld_prec_mod, mld_protect_name => mld_zbjac_aply implicit none ! Arguments type(psb_desc_type), intent(in) :: desc_data type(mld_zbaseprc_type), intent(in) :: prec complex(kind(0.d0)),intent(in) :: x(:) complex(kind(0.d0)),intent(inout) :: y(:) complex(kind(0.d0)),intent(in) :: alpha,beta character(len=1), intent(in) :: trans complex(kind(0.d0)),target, intent(inout) :: work(:) integer, intent(out) :: info ! Local variables integer :: n_row,n_col complex(kind(1.d0)), pointer :: ww(:), aux(:), tx(:),ty(:) integer :: ictxt,np,me,i, err_act character(len=20) :: name character :: trans_ interface subroutine mld_zumf_solve(flag,m,x,b,n,ptr,info) integer, intent(in) :: flag,m,n,ptr integer, intent(out) :: info complex(kind(1.d0)), intent(in) :: b(*) complex(kind(1.d0)), intent(inout) :: x(*) end subroutine mld_zumf_solve end interface name='mld_zbjac_aply' info = 0 call psb_erractionsave(err_act) ictxt=psb_cd_get_context(desc_data) call psb_info(ictxt, me, np) trans_ = 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='complex(kind(1.d0))') 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='complex(kind(1.d0))') goto 9999 end if endif if (prec%iprcparm(mld_smooth_sweeps_) == 1) then ! ! TASKS 1, 3 and 4 ! 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(zone,prec%av(mld_l_pr_),x,zzero,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(zone,prec%av(mld_u_pr_),x,zzero,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_zslu_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info) case('T') call mld_zslu_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info) case('C') call mld_zslu_solve(2,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_zsludist_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info) case('T') call mld_zsludist_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info) case('C') call mld_zsludist_solve(2,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_zumf_solve(0,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info) case('T') call mld_zumf_solve(1,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info) case('C') call mld_zumf_solve(2,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 Jacobi Sweeps = 1') goto 9999 endif else if (prec%iprcparm(mld_smooth_sweeps_) > 1) then ! ! TASK 2 ! ! Apply prec%iprcparm(smooth_sweeps_) sweeps of a block-Jacobi solver ! to compute an approximate solution of a linear system. ! ! Note: trans is always 'N' here. ! if (size(prec%av) < mld_ap_nd_) then info = 4011 goto 9999 endif allocate(tx(n_col),ty(n_col),stat=info) if (info /= 0) then info=4025 call psb_errpush(info,name,i_err=(/2*n_col,0,0,0,0/),& & a_err='complex(kind(1.d0))') goto 9999 end if select case(prec%iprcparm(mld_sub_solve_)) case(mld_ilu_n_,mld_milu_n_,mld_ilu_t_) ! ! Use ILU(k)/MILU(k)/ILU(k,t) on the blocks. ! select case(trans_) case('N') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(j+1) = D^(-1)*(X-ND*Y(j)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux) if (info /=0) exit call psb_spsm(zone,prec%av(mld_l_pr_),ty,zzero,ww,& & prec%desc_data,info,& & trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux) if (info /=0) exit call psb_spsm(zone,prec%av(mld_u_pr_),ww,zzero,tx,& & prec%desc_data,info,& & trans=trans_,unit='U',choice=psb_none_,work=aux) if (info /=0) exit end do case('T','C') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(j+1) = D^(-1)*(X-ND*Y(j)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux,trans=trans_) if (info /=0) exit call psb_spsm(zone,prec%av(mld_u_pr_),ty,zzero,ww,& & prec%desc_data,info,& & trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux) if (info /=0) exit call psb_spsm(zone,prec%av(mld_l_pr_),ww,zzero,tx,& & prec%desc_data,info,& & trans=trans_,unit='U',choice=psb_none_,work=aux) if (info /=0) exit end do case default call psb_errpush(4001,name,a_err='Invalid TRANS in ILU subsolve') goto 9999 end select case(mld_sludist_) ! ! Wrong choice: SuperLU_DIST ! info = 4001 call psb_errpush(4001,name,a_err='Invalid SuperLU_DIST with Jacobi sweeps >1') goto 9999 case(mld_slu_) ! ! Use the LU factorization from SuperLU. ! select case(trans_) case('N') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux) if (info /= 0) exit call mld_zslu_solve(0,n_row,1,ty,n_row,prec%iprcparm(mld_slu_ptr_),info) if (info /= 0) exit tx(1:n_row) = ty(1:n_row) end do case('T') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux,trans=trans_) if (info /= 0) exit call mld_zslu_solve(1,n_row,1,ty,n_row,prec%iprcparm(mld_slu_ptr_),info) if (info /= 0) exit tx(1:n_row) = ty(1:n_row) end do case('C') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux,trans=trans_) if (info /= 0) exit call mld_zslu_solve(2,n_row,1,ty,n_row,prec%iprcparm(mld_slu_ptr_),info) if (info /= 0) exit tx(1:n_row) = ty(1:n_row) end do case default call psb_errpush(4001,name,a_err='Invalid TRANS in SLU subsolve') goto 9999 end select case(mld_umf_) ! ! Use the LU factorization from UMFPACK. ! select case(trans_) case('N') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux) if (info /= 0) exit call mld_zumf_solve(0,n_row,ww,ty,n_row,& & prec%iprcparm(mld_umf_numptr_),info) if (info /= 0) exit tx(1:n_row) = ww(1:n_row) end do case('T') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux,trans=trans_) if (info /= 0) exit call mld_zumf_solve(1,n_row,ww,ty,n_row,& & prec%iprcparm(mld_umf_numptr_),info) if (info /= 0) exit tx(1:n_row) = ww(1:n_row) end do case('C') tx = zzero ty = zzero do i=1, prec%iprcparm(mld_smooth_sweeps_) ! ! Compute Y(k+1) = D^(-1)*(X-ND*Y(k)), where D and ND are the ! block diagonal part and the remaining part of the local matrix ! and Y(j) is the approximate solution at sweep j. ! ty(1:n_row) = x(1:n_row) call psb_spmm(-zone,prec%av(mld_ap_nd_),tx,zone,ty,& & prec%desc_data,info,work=aux,trans=trans_) if (info /= 0) exit call mld_zumf_solve(2,n_row,ww,ty,n_row,& & prec%iprcparm(mld_umf_numptr_),info) if (info /= 0) exit tx(1:n_row) = ww(1:n_row) end do case default call psb_errpush(4001,name,a_err='Invalid TRANS in UMF subsolve') goto 9999 end select case default call psb_errpush(4001,name,a_err='Invalid mld_sub_solve_') goto 9999 end select if (info /= 0) then info=4001 call psb_errpush(info,name,a_err='subsolve with Jacobi sweeps > 1') goto 9999 end if ! ! Put the result into the output vector Y. ! call psb_geaxpby(alpha,tx,beta,y,desc_data,info) deallocate(tx,ty,stat=info) if (info /= 0) then info=4001 call psb_errpush(info,name,a_err='final cleanup with Jacobi sweeps > 1') goto 9999 end if else info = 10 call psb_errpush(info,name,& & i_err=(/2,prec%iprcparm(mld_smooth_sweeps_),0,0,0/)) 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_zbjac_aply