!!$ !!$ !!$ 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 University of Campania "L. Vanvitelli", Caserta !!$ !!$ 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_zaggrmat_minnrg_asb.F90 ! ! Subroutine: mld_zaggrmat_minnrg_asb ! Version: complex ! ! 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_zprecinit and mld_zprecset. ! 4. Minimum energy aggregation: ADD REFERENCE. ! 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_z_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_zspmat_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_z_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_dml_parms), input ! Parameters controlling the choice of algorithm ! ac - type(psb_zspmat_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_zspmat_type), input/output ! The tentative prolongator on input, the computed prolongator on output ! ! op_restr - type(psb_zspmat_type), output ! The restrictor operator; normally, it is the transpose of the prolongator. ! ! info - integer, output. ! Error code. ! ! subroutine mld_zaggrmat_minnrg_asb(a,desc_a,ilaggr,nlaggr,parms,ac,op_prol,op_restr,info) use psb_base_mod use mld_z_inner_mod, mld_protect_name => mld_zaggrmat_minnrg_asb implicit none ! Arguments type(psb_zspmat_type), intent(in) :: a type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_), intent(inout) :: ilaggr(:), nlaggr(:) type(mld_dml_parms), intent(inout) :: parms type(psb_zspmat_type), intent(inout) :: op_prol type(psb_zspmat_type), intent(out) :: ac,op_restr integer(psb_ipk_), intent(out) :: info ! Local variables integer(psb_ipk_), allocatable :: nzbr(:), idisp(:) integer(psb_ipk_) :: nrow, nglob, ncol, ntaggr, nzac, ip, ndx,& & naggr, nzl,naggrm1,naggrp1, i, j, k, jd, icolF, nrt, err_act integer(psb_ipk_) :: ictxt,np,me, icomm character(len=20) :: name type(psb_zspmat_type) :: af, ptilde, rtilde, atran, atp, atdatp type(psb_zspmat_type) :: am3,am4, ap, adap,atmp,rada, ra, atmp2, dap, dadap, da type(psb_zspmat_type) :: dat, datp, datdatp, atmp3, tmp_prol type(psb_z_coo_sparse_mat) :: tmpcoo type(psb_z_csr_sparse_mat) :: acsr1, acsr2, acsr3, acsr, acsrf type(psb_z_csc_sparse_mat) :: csc_dap, csc_dadap, csc_datp, csc_datdatp, acsc complex(psb_dpk_), allocatable :: adiag(:), adinv(:) complex(psb_dpk_), allocatable :: omf(:), omp(:), omi(:), oden(:) logical :: filter_mat integer(psb_ipk_) :: ierr(5) integer(psb_ipk_) :: debug_level, debug_unit integer(psb_ipk_), parameter :: ncmax=16 real(psb_dpk_) :: anorm, theta complex(psb_dpk_) :: tmp, alpha, beta, ommx name='mld_aggrmat_minnrg' 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() icomm = desc_a%get_mpic() 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) allocate(nzbr(np), idisp(np),stat=info) if (info /= psb_success_) then info=psb_err_alloc_request_; ierr(1)=2*np; call psb_errpush(info,name,i_err=ierr,a_err='integer') goto 9999 end if 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. ! allocate(adinv(ncol),& & omf(ncol),omp(ntaggr),oden(ntaggr),omi(ncol),stat=info) if (info /= psb_success_) then info=psb_err_alloc_request_; ierr(1)=6*ncol+ntaggr; call psb_errpush(info,name,i_err=ierr,a_err='complex(psb_dpk_)') goto 9999 end if ! 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) do i=1,size(adiag) if (adiag(i) /= zzero) then adinv(i) = zone / adiag(i) else adinv(i) = zone end if end do 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(tmpcoo) call ptilde%cscnv(info,type='csr') if (info == psb_success_) call a%cscnv(am3,info,type='csr',dupl=psb_dupl_add_) if (info == psb_success_) call a%cscnv(da,info,type='csr',dupl=psb_dupl_add_) if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='spcnv') goto 9999 end if if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & ' Initial copies done.' call da%scal(adinv,info) call psb_symbmm(da,ptilde,dap,info) if (info == psb_success_) call psb_numbmm(da,ptilde,dap) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='symbmm 1') goto 9999 end if call dap%clone(atmp,info) call psb_sphalo(atmp,desc_a,am4,info,& & colcnv=.false.,rowscale=.true.,outfmt='CSR ') if (info == psb_success_) call psb_rwextd(ncol,atmp,info,b=am4) if (info == psb_success_) call am4%free() call psb_symbmm(da,atmp,dadap,info) call psb_numbmm(da,atmp,dadap) call atmp%free() ! !$ write(0,*) 'Columns of AP',psb_sp_get_ncols(ap) ! !$ write(0,*) 'Columns of ADAP',psb_sp_get_ncols(adap) call dap%mv_to(csc_dap) call dadap%mv_to(csc_dadap) call csc_mat_col_prod(csc_dap,csc_dadap,omp,info) call csc_mat_col_prod(csc_dadap,csc_dadap,oden,info) call psb_sum(ictxt,omp) call psb_sum(ictxt,oden) ! !$ write(0,*) trim(name),' OMP :',omp ! !$ write(0,*) trim(name),' ODEN:',oden omp = omp/oden ! !$ write(0,*) 'Check on output prolongator ',omp(1:min(size(omp),10)) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 1' call am3%mv_to(acsr3) ! Compute omega_int ommx = zzero do i=1, ncol omi(i) = omp(ilaggr(i)) if(abs(omi(i)) .gt. abs(ommx)) ommx = omi(i) end do ! Compute omega_fine do i=1, nrow omf(i) = ommx do j=acsr3%irp(i),acsr3%irp(i+1)-1 if(abs(omi(acsr3%ja(j))) .lt. abs(omf(i))) omf(i)=omi(acsr3%ja(j)) end do !!$ if(min(real(omf(i)),aimag(omf(i))) < dzero) omf(i) = zzero if(psb_minreal(omf(i)) < dzero) omf(i) = zzero end do omf(1:nrow) = omf(1:nrow) * adinv(1:nrow) if (filter_mat) then ! ! Build the filtered matrix Af from A ! call a%cscnv(acsrf,info,dupl=psb_dupl_add_) do i=1,nrow tmp = zzero 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)=zzero 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) ! ! 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) = zone - omf(i)*acsrf%val(j) else acsrf%val(j) = - omf(i)*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 SYMBMM 1' call af%mv_from(acsrf) ! ! Symbmm90 does the allocation for its result. ! ! op_prol = (I-w*D*Af)Ptilde ! Doing it this way means to consider diag(Af_i) ! ! call psb_symbmm(af,ptilde,op_prol,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='symbmm 1') goto 9999 end if call psb_numbmm(af,ptilde,op_prol) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 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) = zone - omf(i)*acsr3%val(j) else acsr3%val(j) = - omf(i)*acsr3%val(j) end if end do end do call am3%mv_from(acsr3) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done gather, going for SYMBMM 1' ! ! Symbmm90 does the allocation for its result. ! ! op_prol = (I-w*D*A)Ptilde ! ! call psb_symbmm(am3,ptilde,op_prol,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='symbmm 1') goto 9999 end if call psb_numbmm(am3,ptilde,op_prol) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 1' end if ! ! Ok, let's start over with the restrictor ! call ptilde%transc(rtilde) call a%cscnv(atmp,info,type='csr') call psb_sphalo(atmp,desc_a,am4,info,& & colcnv=.true.,rowscale=.true.) nrt = am4%get_nrows() call am4%csclip(atmp2,info,ione,nrt,ione,ncol) call atmp2%cscnv(info,type='CSR') if (info == psb_success_) call psb_rwextd(ncol,atmp,info,b=atmp2) call am4%free() call atmp2%free() ! This is to compute the transpose. It ONLY works if the ! original A has a symmetric pattern. call atmp%transc(atmp2) call atmp2%csclip(dat,info,ione,nrow,ione,ncol) call dat%cscnv(info,type='csr') call dat%scal(adinv,info) ! Now for the product. call psb_symbmm(dat,ptilde,datp,info) if (info == psb_success_) call psb_numbmm(dat,ptilde,datp) call datp%clone(atmp2,info) call psb_sphalo(atmp2,desc_a,am4,info,& & colcnv=.false.,rowscale=.true.,outfmt='CSR ') if (info == psb_success_) call psb_rwextd(ncol,atmp2,info,b=am4) if (info == psb_success_) call am4%free() call psb_symbmm(dat,atmp2,datdatp,info) call psb_numbmm(dat,atmp2,datdatp) call atmp2%free() call datp%mv_to(csc_datp) call datdatp%mv_to(csc_datdatp) call csc_mat_col_prod(csc_datp,csc_datdatp,omp,info) call csc_mat_col_prod(csc_datdatp,csc_datdatp,oden,info) call psb_sum(ictxt,omp) call psb_sum(ictxt,oden) ! !$ write(debug_unit,*) trim(name),' OMP_R :',omp ! ! $ write(debug_unit,*) trim(name),' ODEN_R:',oden omp = omp/oden ! !$ write(0,*) 'Check on output restrictor',omp(1:min(size(omp),10)) ! Compute omega_int ommx = zzero do i=1, ncol omi(i) = omp(ilaggr(i)) if(abs(omi(i)) .gt. abs(ommx)) ommx = omi(i) end do ! Compute omega_fine ! Going over the columns of atmp means going over the rows ! of A^T. Hopefully ;-) call atmp%cp_to(acsc) do i=1, nrow omf(i) = ommx do j= acsc%icp(i),acsc%icp(i+1)-1 if(abs(omi(acsc%ia(j))) .lt. abs(omf(i))) omf(i)=omi(acsc%ia(j)) end do !!$ if(min(real(omf(i)),aimag(omf(i))) < dzero) omf(i) = zzero if(psb_minreal(omf(i)) < dzero) omf(i) = zzero end do omf(1:nrow) = omf(1:nrow)*adinv(1:nrow) call psb_halo(omf,desc_a,info) call acsc%free() call atmp%mv_to(acsr1) do i=1,acsr1%get_nrows() do j=acsr1%irp(i),acsr1%irp(i+1)-1 if (acsr1%ja(j) == i) then acsr1%val(j) = zone - acsr1%val(j)*omf(acsr1%ja(j)) else acsr1%val(j) = - acsr1%val(j)*omf(acsr1%ja(j)) end if end do end do call atmp%mv_from(acsr1) call rtilde%mv_to(tmpcoo) nzl = tmpcoo%get_nzeros() i=0 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 rtilde%mv_from(tmpcoo) call rtilde%cscnv(info,type='csr') call psb_symbmm(rtilde,atmp,op_restr,info) call psb_numbmm(rtilde,atmp,op_restr) ! ! Now we have to gather the halo of op_prol, and add it to itself ! to multiply it by A, ! call op_prol%clone(tmp_prol,info) if (info == psb_success_) 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 op_prol') goto 9999 end if ! ! 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(:) ! call op_restr%mv_to(tmpcoo) nzl = tmpcoo%get_nzeros() i=0 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 op_restr%mv_from(tmpcoo) call op_restr%cscnv(info,type='csr') if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'starting sphalo/ rwxtd' call psb_symbmm(a,tmp_prol,am3,info) if(info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,& & a_err='symbmm 2') goto 9999 end if call psb_numbmm(a,tmp_prol,am3) if (debug_level >= psb_debug_outer_) & & write(debug_unit,*) me,' ',trim(name),& & 'Done NUMBMM 2' 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),& & 'Done sphalo/ rwxtd' call psb_symbmm(op_restr,am3,ac,info) if (info == psb_success_) call psb_numbmm(op_restr,am3,ac) if (info == psb_success_) call am3%free() if (info == psb_success_) call ac%cscnv(info,type='coo',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 contains subroutine csc_mat_col_prod(a,b,v,info) implicit none type(psb_z_csc_sparse_mat), intent(in) :: a, b complex(psb_dpk_), intent(out) :: v(:) integer(psb_ipk_), intent(out) :: info integer(psb_ipk_) :: i,j,k, nr, nc,iap,nra,ibp,nrb info = psb_success_ nc = a%get_ncols() if (nc /= b%get_ncols()) then write(0,*) 'Matrices A and B should have same columns' info = -1 return end if do j=1, nc iap = a%icp(j) nra = a%icp(j+1)-iap ibp = b%icp(j) nrb = b%icp(j+1)-ibp v(j) = sparse_srtd_dot(nra,a%ia(iap:iap+nra-1),a%val(iap:iap+nra-1),& & nrb,b%ia(ibp:ibp+nrb-1),b%val(ibp:ibp+nrb-1)) end do end subroutine csc_mat_col_prod subroutine csr_mat_row_prod(a,b,v,info) implicit none type(psb_z_csr_sparse_mat), intent(in) :: a, b complex(psb_dpk_), intent(out) :: v(:) integer(psb_ipk_), intent(out) :: info integer(psb_ipk_) :: i,j,k, nr, nc,iap,nca,ibp,ncb info = psb_success_ nr = a%get_nrows() if (nr /= b%get_nrows()) then write(0,*) 'Matrices A and B should have same rows' info = -1 return end if do j=1, nr iap = a%irp(j) nca = a%irp(j+1)-iap ibp = b%irp(j) ncb = b%irp(j+1)-ibp v(j) = sparse_srtd_dot(nca,a%ja(iap:iap+nca-1),a%val(iap:iap+nca-1),& & ncb,b%ja(ibp:ibp+ncb-1),b%val(ibp:ibp+ncb-1)) end do end subroutine csr_mat_row_prod function sparse_srtd_dot(nv1,iv1,v1,nv2,iv2,v2) result(dot) implicit none integer(psb_ipk_), intent(in) :: nv1,nv2 integer(psb_ipk_), intent(in) :: iv1(:), iv2(:) complex(psb_dpk_), intent(in) :: v1(:),v2(:) complex(psb_dpk_) :: dot integer(psb_ipk_) :: i,j,k, ip1, ip2 dot = zzero ip1 = 1 ip2 = 1 do if (ip1 > nv1) exit if (ip2 > nv2) exit if (iv1(ip1) == iv2(ip2)) then dot = dot + conjg(v1(ip1))*v2(ip2) ip1 = ip1 + 1 ip2 = ip2 + 1 else if (iv1(ip1) < iv2(ip2)) then ip1 = ip1 + 1 else ip2 = ip2 + 1 end if end do end function sparse_srtd_dot subroutine local_dump(me,mat,name,header) type(psb_zspmat_type), intent(in) :: mat integer(psb_ipk_), intent(in) :: me character(len=*), intent(in) :: name character(len=*), intent(in) :: header character(len=80) :: filename write(filename,'(a,a,i0,a,i0,a)') trim(name),'.p',me open(20+me,file=filename) call mat%print(20+me,head=trim(header)) close(20+me) end subroutine local_dump end subroutine mld_zaggrmat_minnrg_asb