! ! Parallel Sparse BLAS version 3.5 ! (C) Copyright 2006-2018 ! Salvatore Filippone ! Alfredo Buttari ! ! 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 PSBLAS 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 PSBLAS 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. ! ! Moved here from AMG4PSBLAS, original copyright below. ! ! ! AMG-AINV: Approximate Inverse plugin for ! AMG4PSBLAS version 1.0 ! ! (C) Copyright 2020 ! ! 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 AMG4PSBLAS 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 AMG4PSBLAS 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. ! ! subroutine psb_z_invt_bld(a,fillin,invfill,thresh,invthresh,& & lmat,d,umat,desc,info,blck) use psb_base_mod use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_bld use psb_z_ilu_fact_mod implicit none ! Arguments type(psb_zspmat_type), intent(in), target :: a integer(psb_ipk_), intent(in) :: fillin,invfill real(psb_dpk_), intent(in) :: thresh real(psb_dpk_), intent(in) :: invthresh type(psb_zspmat_type), intent(inout) :: lmat, umat complex(psb_dpk_), allocatable :: d(:) Type(psb_desc_type), Intent(inout) :: desc integer(psb_ipk_), intent(out) :: info type(psb_zspmat_type), intent(in), optional :: blck ! integer(psb_ipk_) :: i, nztota, err_act, n_row, nrow_a, n_col type(psb_zspmat_type) :: atmp complex(psb_dpk_), allocatable :: pq(:), pd(:), w(:) integer(psb_ipk_) :: debug_level, debug_unit integer(psb_ipk_) :: ictxt,np,me integer(psb_ipk_) :: nzrmax real(psb_dpk_) :: sp_thresh character(len=20) :: name, ch_err, fname info = psb_success_ name='psb_zinvt_fact' call psb_erractionsave(err_act) if (psb_errstatus_fatal()) then info = psb_err_internal_error_; goto 9999 end if debug_unit = psb_get_debug_unit() debug_level = psb_get_debug_level() ictxt = psb_cd_get_context(desc) call psb_info(ictxt, me, np) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),' start' ! ! Check the memory available to hold the incomplete L and U factors ! and allocate it if needed ! nrow_a = a%get_nrows() nztota = a%get_nzeros() if (present(blck)) then nztota = nztota + blck%get_nzeros() end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & ': out get_nnzeros',nrow_a,nztota,& & a%get_nrows(),a%get_ncols(),a%get_nzeros() n_row = psb_cd_get_local_rows(desc) n_col = psb_cd_get_local_cols(desc) allocate(pd(n_row),w(n_row),stat=info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') goto 9999 end if nzrmax = fillin sp_thresh = thresh call lmat%allocate(n_row,n_row,info,nz=nztota) if (info == psb_success_) call umat%allocate(n_row,n_row,info,nz=nztota) if (info == 0) call psb_ilut_fact(nzrmax,sp_thresh,& & a,lmat,umat,pd,info,blck=blck,iscale=psb_ilu_scale_maxval_) if (info == psb_success_) call atmp%allocate(n_row,n_row,info,nz=nztota) if(info/=0) then info=psb_err_from_subroutine_ ch_err='psb_sp_all' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if if (.false.) then !!$ if (debug_level >= psb_debug_inner_) then write(fname,'(a,i0,a)') 'invt-lo-',me,'.mtx' call lmat%print(fname,head="INVTLOW") write(fname,'(a,i0,a)') 'invt-up-',me,'.mtx' call umat%print(fname,head="INVTUPP") end if ! ! Compute the approx U^-1 and L^-1 ! nzrmax = invfill call psb_zsparse_invt(n_row,umat,atmp,nzrmax,invthresh,info) if (info == psb_success_) call psb_move_alloc(atmp,umat,info) if (info == psb_success_) call lmat%transp() if (info == psb_success_) call psb_zsparse_invt(n_row,lmat,atmp,nzrmax,invthresh,info) if (info == psb_success_) call psb_move_alloc(atmp,lmat,info) if (info == psb_success_) call lmat%transp() ! Done. Hopefully.... if (info /= psb_success_) then info = psb_err_internal_error_ call psb_errpush(info,name,a_err='invt') goto 9999 end if call psb_move_alloc(pd,d,info) call lmat%set_asb() call lmat%trim() call umat%set_asb() call umat%trim() if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),' end' call psb_erractionrestore(err_act) return 9999 call psb_error_handler(err_act) return end subroutine psb_z_invt_bld subroutine psb_zsparse_invt(n,a,z,nzrmax,sp_thresh,info) use psb_base_mod use psb_z_invt_fact_mod, psb_protect_name => psb_zsparse_invt implicit none integer(psb_ipk_), intent(in) :: n type(psb_zspmat_type), intent(in) :: a type(psb_zspmat_type), intent(inout) :: z integer(psb_ipk_), intent(in) :: nzrmax real(psb_dpk_), intent(in) :: sp_thresh integer(psb_ipk_), intent(out) :: info ! integer(psb_ipk_) :: i,j,k, err_act, nz, nzra, nzrz, ipz1,ipz2, nzz, ip1, ip2, l2 integer(psb_ipk_), allocatable :: ia(:), ja(:), iz(:),jz(:) complex(psb_dpk_), allocatable :: zw(:), val(:), valz(:) integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:) complex(psb_dpk_), allocatable :: row(:) type(psb_z_coo_sparse_mat) :: trw type(psb_z_csr_sparse_mat) :: acsr, zcsr integer(psb_ipk_) :: ktrw, nidx, nlw,nup,jmaxup type(psb_i_heap) :: heap real(psb_dpk_) :: alpha, nrmi character(len=20) :: name='psb_sp_invt' info = psb_success_ call psb_erractionsave(err_act) if (psb_errstatus_fatal()) then info = psb_err_internal_error_; goto 9999 end if if (.not.(a%is_triangle().and.a%is_unit().and.a%is_upper())) then write(psb_err_unit,*) 'Wrong A ' info = psb_err_internal_error_ call psb_errpush(psb_err_internal_error_,name,a_err='wrong A') goto 9999 end if call a%cp_to(acsr) call trw%allocate(izero,izero,ione) if (info == psb_success_) allocate(zw(n),iz(n),valz(n),& & row(n),rowlevs(n),stat=info) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') goto 9999 end if call zcsr%allocate(n,n,n*nzrmax) call zcsr%set_triangle() call zcsr%set_unit(.false.) call zcsr%set_upper() ! ! nzz = 0 row(:) = zzero rowlevs(:) = 0 l2 = 0 zcsr%irp(1) = 1 outer: do i = 1, n-1 ! ZW = e_i call psb_z_invt_copyin(i,n,acsr,i,ione,n,nlw,nup,jmaxup,nrmi,row,& & heap,rowlevs,ktrw,trw,info,sign=-done) if (info /= 0) exit row(i) = zone ! Adjust norm if (nrmi < done) then nrmi = sqrt(done + nrmi**2) else nrmi = nrmi*sqrt(zone+zone/(nrmi**2)) end if call psb_invt_inv(sp_thresh,i,nrmi,row,heap,rowlevs,& & acsr%ja,acsr%irp,acsr%val,nidx,idxs,info) if (info /= 0) exit !!$ write(0,*) 'Calling copyout ',nzrmax,nlw,nup,nidx,l2 call psb_z_invt_copyout(nzrmax,sp_thresh,i,n,nlw,nup,jmaxup,nrmi,row,& & nidx,idxs,l2,zcsr%ja,zcsr%irp,zcsr%val,info) if (info /= 0) exit nzz = l2 end do outer if (info /= psb_success_) then info = psb_err_internal_error_ call psb_errpush(info,name,a_err='mainloop') goto 9999 end if ipz1 = nzz+1 call psb_ensure_size(ipz1,zcsr%val,info) call psb_ensure_size(ipz1,zcsr%ja,info) zcsr%val(ipz1) = zone zcsr%ja(ipz1) = n zcsr%irp(n+1) = ipz1+1 call z%mv_from(zcsr) call psb_erractionrestore(err_act) return 9999 call psb_error_handler(err_act) return end subroutine psb_zsparse_invt subroutine psb_z_invt_copyin(i,m,a,jd,jmin,jmax,nlw,nup,jmaxup,nrmi,row,heap,& & irwt,ktrw,trw,info,sign) use psb_base_mod use psb_d_invt_fact_mod, psb_protect_name => psb_d_invt_copyin implicit none type(psb_z_csr_sparse_mat), intent(in) :: a type(psb_z_coo_sparse_mat), intent(inout) :: trw integer(psb_ipk_), intent(in) :: i, m,jmin,jmax,jd integer(psb_ipk_), intent(inout) :: ktrw,nlw,nup,jmaxup,info integer(psb_ipk_), intent(inout) :: irwt(:) real(psb_dpk_), intent(inout) :: nrmi complex(psb_dpk_), intent(inout) :: row(:) type(psb_i_heap), intent(inout) :: heap real(psb_dpk_), intent(in), optional :: sign ! integer(psb_ipk_) :: k,j,irb,kin,nz, err_act integer(psb_ipk_), parameter :: nrb=16 real(psb_dpk_) :: dmaxup, sign_ real(psb_dpk_), external :: dnrm2 character(len=20), parameter :: name='invt_copyin' info = psb_success_ call psb_erractionsave(err_act) if (psb_errstatus_fatal()) then info = psb_err_internal_error_; goto 9999 end if call heap%init(info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_init_heap') goto 9999 end if sign_ = done if (present(sign)) sign_ = sign ! ! nrmi is the norm of the current sparse row (for the time being, ! we use the 2-norm). ! NOTE: the 2-norm below includes also elements that are outside ! [jmin:jmax] strictly. Is this really important? TO BE CHECKED. ! nlw = 0 nup = 0 jmaxup = 0 dmaxup = zzero nrmi = zzero do j = a%irp(i), a%irp(i+1) - 1 k = a%ja(j) if ((jmin<=k).and.(k<=jmax)) then row(k) = sign_ * a%val(j) call heap%insert(k,info) irwt(k) = 1 if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_insert_heap') goto 9999 end if end if if (kjd) then nup = nup + 1 if (abs(row(k))>dmaxup) then jmaxup = k dmaxup = abs(row(k)) end if end if end do nz = a%irp(i+1) - a%irp(i) nrmi = dnrm2(nz,a%val(a%irp(i):),ione) return 9999 call psb_error_handler(err_act) return end subroutine psb_z_invt_copyin subroutine psb_z_invt_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row, & & nidx,idxs,l2,ja,irp,val,info) use psb_base_mod use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_copyout implicit none ! Arguments integer(psb_ipk_), intent(in) :: fill_in,i,m,nidx,nlw,nup,jmaxup integer(psb_ipk_), intent(in) :: idxs(:) integer(psb_ipk_), intent(inout) :: l2, info integer(psb_ipk_), allocatable, intent(inout) :: ja(:),irp(:) real(psb_dpk_), intent(in) :: thres,nrmi complex(psb_dpk_),allocatable, intent(inout) :: val(:) complex(psb_dpk_), intent(inout) :: row(:) ! Local variables real(psb_dpk_),allocatable :: xw(:) integer(psb_ipk_), allocatable :: xwid(:), indx(:) real(psb_dpk_) :: witem, wmin integer(psb_ipk_) :: widx integer(psb_ipk_) :: k,isz,err_act,int_err(5),idxp, nz type(psb_d_idx_heap) :: heap character(len=20), parameter :: name='invt_copyout' character(len=20) :: ch_err logical :: fndmaxup info = psb_success_ call psb_erractionsave(err_act) if (psb_errstatus_fatal()) then info = psb_err_internal_error_; goto 9999 end if ! ! Here we need to apply also the dropping rule base on the fill-in. ! We do it by putting into a heap the elements that are not dropped ! by using the 2-norm rule, and then copying them out. ! ! The heap goes down on the entry absolute value, so the first item ! is the largest absolute value. ! !!$ write(0,*) 'invt_copyout ',nidx,nup+fill_in call heap%init(info,dir=psb_asort_down_) if (info == psb_success_) allocate(xwid(nidx),xw(nidx),indx(nidx),stat=info) if (info /= psb_success_) then info=psb_err_alloc_request_ call psb_errpush(info,name,i_err=(/3*nidx/),& & a_err='real(psb_dpk_)') goto 9999 end if ! ! First the lower part ! nz = 0 idxp = 0 do idxp = idxp + 1 if (idxp > nidx) exit if (idxs(idxp) >= i) exit widx = idxs(idxp) witem = row(widx) ! ! Dropping rule based on the 2-norm ! if (abs(witem) < thres*nrmi) cycle nz = nz + 1 xw(nz) = witem xwid(nz) = widx call heap%insert(witem,widx,info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_insert_heap') goto 9999 end if end do if (nz > 1) then write(psb_err_unit,*) 'Warning: lower triangle from invt???? ' end if if (idxp <= size(idxs)) then if (idxs(idxp) < i) then do idxp = idxp + 1 if (idxp > nidx) exit if (idxs(idxp) >= i) exit end do end if end if idxp = idxp - 1 nz = 0 wmin=HUGE(wmin) if (.false.) then do idxp = idxp + 1 if (idxp > nidx) exit widx = idxs(idxp) if (widx < i) then write(psb_err_unit,*) 'Warning: lower triangle in upper copy',widx,i,idxp,idxs(idxp) cycle end if if (widx > m) then cycle end if witem = row(widx) ! ! Dropping rule based on the 2-norm. But keep the jmaxup-th entry anyway. ! if ((widx /= jmaxup) .and. (widx /= i) .and. (abs(witem) < thres*nrmi)) then cycle end if if ((widx/=jmaxup).and.(nz > nup+fill_in)) then if (abs(witem) < wmin) cycle endif wmin = min(abs(witem),wmin) nz = nz + 1 xw(nz) = witem xwid(nz) = widx call heap%insert(witem,widx,info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_insert_heap') goto 9999 end if end do ! ! Now we have to take out the first nup-fill_in entries. But make sure ! we include entry jmaxup. ! if (nz <= nup+fill_in) then ! ! Just copy everything from xw ! fndmaxup=.true. else fndmaxup = .false. nz = nup+fill_in do k=1,nz call heap%get_first(witem,widx,info) xw(k) = witem xwid(k) = widx if (widx == jmaxup) fndmaxup=.true. end do end if if ((i nidx) exit widx = idxs(idxp) if (widx < i) then write(psb_err_unit,*) 'Warning: lower triangle in upper copy',widx,i,idxp,idxs(idxp) cycle end if if (widx > m) then cycle end if witem = row(widx) ! ! Dropping rule based on the 2-norm. But keep the jmaxup-th entry anyway. ! if ((widx /= i) .and. (abs(witem) < thres*nrmi)) then cycle end if if (nz > nup+fill_in) then if (abs(witem) < wmin) cycle endif wmin = min(abs(witem),wmin) nz = nz + 1 xw(nz) = witem xwid(nz) = widx call heap%insert(witem,widx,info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='psb_insert_heap') goto 9999 end if end do ! ! Now we have to take out the first nup-fill_in entries. But make sure ! we include entry jmaxup. ! if (nz > nup+fill_in) then nz = nup+fill_in do k=1,nz call heap%get_first(witem,widx,info) xw(k) = witem xwid(k) = widx end do end if end if ! ! Now we put things back into ascending column order ! call psb_msort(xwid(1:nz),indx(1:nz),dir=psb_sort_up_) ! ! Copy out the upper part of the row ! do k=1,nz l2 = l2 + 1 if (size(val) < l2) then ! ! Figure out a good reallocation size! ! isz = max(int(1.2*l2),l2+100) call psb_realloc(isz,val,info) if (info == psb_success_) call psb_realloc(isz,ja,info) if (info /= psb_success_) then info=psb_err_from_subroutine_ call psb_errpush(info,name,a_err='Allocate') goto 9999 end if end if ja(l2) = xwid(k) val(l2) = xw(indx(k)) end do ! ! Set row to zero ! do idxp=1,nidx row(idxs(idxp)) = zzero end do irp(i+1) = l2 + 1 call psb_erractionrestore(err_act) return 9999 call psb_error_handler(err_act) return end subroutine psb_z_invt_copyout subroutine psb_z_invt_inv(thres,i,nrmi,row,heap,irwt,ja,irp,val,nidx,idxs,info) use psb_base_mod use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_inv implicit none ! Arguments type(psb_i_heap), intent(inout) :: heap integer(psb_ipk_), intent(in) :: i integer(psb_ipk_), intent(inout) :: nidx,info integer(psb_ipk_), intent(inout) :: irwt(:) real(psb_dpk_), intent(in) :: thres,nrmi integer(psb_ipk_), allocatable, intent(inout) :: idxs(:) integer(psb_ipk_), intent(in) :: ja(:),irp(:) complex(psb_dpk_), intent(in) :: val(:) complex(psb_dpk_), intent(inout) :: row(:) ! Local Variables integer(psb_ipk_) :: k,j,jj,lastk,iret real(psb_dpk_) :: rwk, alpha info = psb_success_ call psb_ensure_size(200, idxs, info) if (info /= psb_success_) return nidx = 1 idxs(1) = i lastk = i irwt(i) = 1 !!$ write(0,*) 'Drop Threshold ',thres*nrmi ! ! Do while there are indices to be processed ! do call heap%get_first(k,iret) if (iret < 0) exit ! ! An index may have been put on the heap more than once. ! Should not happen, but just in case. ! if (k == lastk) cycle lastk = k ! ! Dropping rule based on the threshold: compare the absolute ! value of each updated entry of row with thres * 2-norm of row. ! rwk = row(k) if (abs(rwk) < thres*nrmi) then ! ! Drop the entry. ! row(k) = dzero irwt(k) = 0 cycle else ! ! Note: since U is scaled while copying it out (see ilut_copyout), ! we can use rwk in the update below. ! do jj=irp(k),irp(k+1)-1 j = ja(jj) if (j<=k) then info = -i return endif ! ! Update row(j) and, if it is not to be discarded, insert ! its index into the heap for further processing. ! row(j) = row(j) - rwk * val(jj) if (irwt(j) == 0) then if (abs(row(j)) < thres*nrmi) then ! ! Drop the entry. ! row(j) = dzero else ! ! Do the insertion. ! call heap%insert(j,info) if (info /= psb_success_) return irwt(j) = 1 end if end if end do end if ! ! If we get here it is an index we need to keep on copyout. ! nidx = nidx + 1 call psb_ensure_size(nidx,idxs,info,addsz=psb_heap_resize) if (info /= psb_success_) return idxs(nidx) = k irwt(k) = 0 end do irwt(i) = 0 end subroutine psb_z_invt_inv