!!$ !!$ Parallel Sparse BLAS version 2.3.1 !!$ (C) Copyright 2006, 2007, 2008, 2009, 2010 !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari CNRS-IRIT, Toulouse !!$ !!$ 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: ppde.f90 ! ! Program: ppde ! This sample program solves a linear system obtained by discretizing a ! PDE with Dirichlet BCs. ! ! ! The PDE is a general second order equation in 3d ! ! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u) ! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u = 0 ! dxdx dydy dzdz dx dy dz ! ! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1. ! ! Example taken from: ! C.T.Kelley ! Iterative Methods for Linear and Nonlinear Equations ! SIAM 1995 ! ! In this sample program the index space of the discretized ! computational domain is first numbered sequentially in a standard way, ! then the corresponding vector is distributed according to a BLOCK ! data distribution. ! ! Boundary conditions are set in a very simple way, by adding ! equations of the form ! ! u(x,y) = exp(-x^2-y^2-z^2) ! ! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation. ! program ppde use psb_sparse_mod use psb_prec_mod use psb_krylov_mod implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer :: idim ! miscellaneous real(psb_dpk_), parameter :: one = 1.d0 real(psb_dpk_) :: t1, t2, tprec ! sparse matrix and preconditioner type(psb_d_sparse_mat) :: a type(psb_dprec_type) :: prec ! descriptor type(psb_desc_type) :: desc_a ! dense matrices real(psb_dpk_), allocatable :: b(:), x(:) ! blacs parameters integer :: ictxt, iam, np ! solver parameters integer :: iter, itmax,itrace, istopc, irst integer(psb_long_int_k_) :: amatsize, precsize, descsize real(psb_dpk_) :: err, eps ! other variables integer :: info, i character(len=20) :: name,ch_err info=psb_success_ 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 if(psb_get_errstatus() /= 0) goto 9999 name='pde90' call psb_set_errverbosity(2) ! ! get parameters ! call get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst) ! ! allocate and fill in the coefficient matrix, rhs and initial guess ! call psb_barrier(ictxt) t1 = psb_wtime() call create_matrix(idim,a,b,x,desc_a,ictxt,afmt,info) call psb_barrier(ictxt) t2 = psb_wtime() - t1 if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='create_matrix' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if if (iam == psb_root_) write(psb_out_unit,'("Overall matrix creation time : ",es12.5)')t2 if (iam == psb_root_) write(psb_out_unit,'(" ")') ! ! prepare the preconditioner. ! if(iam == psb_root_) write(psb_out_unit,'("Setting preconditioner to : ",a)')ptype call psb_precinit(prec,ptype,info) call psb_barrier(ictxt) t1 = psb_wtime() call psb_precbld(a,desc_a,prec,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='psb_precbld' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tprec = psb_wtime()-t1 call psb_amx(ictxt,tprec) if (iam == psb_root_) write(psb_out_unit,'("Preconditioner time : ",es12.5)')tprec if (iam == psb_root_) write(psb_out_unit,'(" ")') ! ! iterative method parameters ! if(iam == psb_root_) write(psb_out_unit,'("Calling iterative method ",a)')kmethd call psb_barrier(ictxt) t1 = psb_wtime() eps = 1.d-9 call psb_krylov(kmethd,a,prec,b,x,eps,desc_a,info,& & itmax=itmax,iter=iter,err=err,itrace=itrace,istop=istopc,irst=irst) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='solver routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if call psb_barrier(ictxt) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) amatsize = psb_sizeof(a) descsize = psb_sizeof(desc_a) precsize = psb_sizeof(prec) call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) call psb_sum(ictxt,precsize) if (iam == psb_root_) then write(psb_out_unit,'(" ")') write(psb_out_unit,'("Time to solve matrix : ",es12.5)')t2 write(psb_out_unit,'("Time per iteration : ",es12.5)')t2/iter write(psb_out_unit,'("Number of iterations : ",i0)')iter write(psb_out_unit,'("Convergence indicator on exit : ",es12.5)')err write(psb_out_unit,'("Info on exit : ",i0)')info write(psb_out_unit,'("Total memory occupation for A: ",i12)')amatsize write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize write(psb_out_unit,'("Total memory occupation for PREC: ",i12)')precsize end if ! ! cleanup storage and exit ! call psb_gefree(b,desc_a,info) call psb_gefree(x,desc_a,info) call psb_spfree(a,desc_a,info) call psb_precfree(prec,info) call psb_cdfree(desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='free routine' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if 9999 continue if(info /= psb_success_) then call psb_error(ictxt) end if call psb_exit(ictxt) stop contains ! ! get iteration parameters from standard input ! subroutine get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst) integer :: ictxt character(len=*) :: kmethd, ptype, afmt integer :: idim, istopc,itmax,itrace,irst integer :: np, iam integer :: intbuf(10), ip call psb_info(ictxt, iam, np) if (iam == 0) then read(psb_inp_unit,*) ip if (ip >= 3) then read(psb_inp_unit,*) kmethd read(psb_inp_unit,*) ptype read(psb_inp_unit,*) afmt ! broadcast parameters to all processors call psb_bcast(ictxt,kmethd) call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,ptype) read(psb_inp_unit,*) idim if (ip >= 4) then read(psb_inp_unit,*) istopc else istopc=1 endif if (ip >= 5) then read(psb_inp_unit,*) itmax else itmax=500 endif if (ip >= 6) then read(psb_inp_unit,*) itrace else itrace=-1 endif if (ip >= 7) then read(psb_inp_unit,*) irst else irst=1 endif ! broadcast parameters to all processors intbuf(1) = idim intbuf(2) = istopc intbuf(3) = itmax intbuf(4) = itrace intbuf(5) = irst call psb_bcast(ictxt,intbuf(1:5)) write(psb_out_unit,'("Solving matrix : ell1")') write(psb_out_unit,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim write(psb_out_unit,'("Number of processors : ",i0)')np write(psb_out_unit,'("Data distribution : BLOCK")') write(psb_out_unit,'("Preconditioner : ",a)') ptype write(psb_out_unit,'("Iterative method : ",a)') kmethd write(psb_out_unit,'(" ")') else ! wrong number of parameter, print an error message and exit call pr_usage(0) call psb_abort(ictxt) stop 1 endif else call psb_bcast(ictxt,kmethd) call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,ptype) call psb_bcast(ictxt,intbuf(1:5)) idim = intbuf(1) istopc = intbuf(2) itmax = intbuf(3) itrace = intbuf(4) irst = intbuf(5) end if return end subroutine get_parms ! ! print an error message ! subroutine pr_usage(iout) integer :: iout write(iout,*)'incorrect parameter(s) found' write(iout,*)' usage: pde90 methd prec dim & &[istop itmax itrace]' write(iout,*)' where:' write(iout,*)' methd: cgstab cgs rgmres bicgstabl' write(iout,*)' prec : bjac diag none' write(iout,*)' dim number of points along each axis' write(iout,*)' the size of the resulting linear ' write(iout,*)' system is dim**3' write(iout,*)' istop stopping criterion 1, 2 ' write(iout,*)' itmax maximum number of iterations [500] ' write(iout,*)' itrace <=0 (no tracing, default) or ' write(iout,*)' >= 1 do tracing every itrace' write(iout,*)' iterations ' end subroutine pr_usage ! ! subroutine to allocate and fill in the coefficient matrix and ! the rhs. ! subroutine create_matrix(idim,a,b,xv,desc_a,ictxt,afmt,info) ! ! discretize the partial diferential equation ! ! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u) ! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u ! dxdx dydy dzdz dx dy dz ! ! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1. ! ! Boundary conditions are set in a very simple way, by adding ! equations of the form ! ! u(x,y) = exp(-x^2-y^2-z^2) ! ! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation. ! use psb_sparse_mod use psb_d_mat_mod implicit none integer :: idim integer, parameter :: nb=20 real(psb_dpk_), allocatable :: b(:),xv(:) type(psb_desc_type) :: desc_a integer :: ictxt, info character :: afmt*5 type(psb_d_sparse_mat) :: a type(psb_d_csc_sparse_mat) :: acsc type(psb_d_coo_sparse_mat) :: acoo type(psb_d_csr_sparse_mat) :: acsr real(psb_dpk_) :: zt(nb),x,y,z integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k integer :: ix,iy,iz,ia,indx_owner integer :: np, iam, nr, nt integer :: element integer, allocatable :: irow(:),icol(:),myidx(:) real(psb_dpk_), allocatable :: val(:) ! deltah dimension of each grid cell ! deltat discretization time real(psb_dpk_) :: deltah real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0 real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3 external :: a1, a2, a3, a4, b1, b2, b3 integer :: err_act character(len=20) :: name, ch_err,tmpfmt info = psb_success_ name = 'create_matrix' call psb_erractionsave(err_act) call psb_info(ictxt, iam, np) deltah = 1.d0/(idim-1) ! initialize array descriptor and sparse matrix storage. provide an ! estimate of the number of non zeroes m = idim*idim*idim n = m nnz = ((n*9)/(np)) if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n ! ! Using a simple BLOCK distribution. ! nt = (m+np-1)/np nr = max(0,min(nt,m-(iam*nt))) nt = nr call psb_sum(ictxt,nt) if (nt /= m) write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m call psb_barrier(ictxt) t0 = psb_wtime() call psb_cdall(ictxt,desc_a,info,nl=nr) if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz) ! define rhs from boundary conditions; also build initial guess if (info == psb_success_) call psb_geall(b,desc_a,info) if (info == psb_success_) call psb_geall(xv,desc_a,info) nlr = psb_cd_get_local_rows(desc_a) call psb_barrier(ictxt) talc = psb_wtime()-t0 if (info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='allocation rout.' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if ! we build an auxiliary matrix consisting of one row at a ! time; just a small matrix. might be extended to generate ! a bunch of rows per call. ! allocate(val(20*nb),irow(20*nb),& &icol(20*nb),myidx(nlr),stat=info) if (info /= psb_success_ ) then info=psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 endif do i=1,nlr myidx(i) = i end do call psb_loc_to_glob(myidx,desc_a,info) ! loop over rows belonging to current process in a block ! distribution. call psb_barrier(ictxt) t1 = psb_wtime() do ii=1, nlr,nb ib = min(nb,nlr-ii+1) element = 1 do k=1,ib i=ii+k-1 ! local matrix pointer glob_row=myidx(i) ! compute gridpoint coordinates if (mod(glob_row,(idim*idim)) == 0) then ix = glob_row/(idim*idim) else ix = glob_row/(idim*idim)+1 endif if (mod((glob_row-(ix-1)*idim*idim),idim) == 0) then iy = (glob_row-(ix-1)*idim*idim)/idim else iy = (glob_row-(ix-1)*idim*idim)/idim+1 endif iz = glob_row-(ix-1)*idim*idim-(iy-1)*idim ! x, y, x coordinates x = ix*deltah y = iy*deltah z = iz*deltah ! check on boundary points zt(k) = 0.d0 ! internal point: build discretization ! ! term depending on (x-1,y,z) ! if (ix == 1) then val(element)=-b1(x,y,z)-a1(x,y,z) val(element) = val(element)/(deltah*& & deltah) zt(k) = exp(-y**2-z**2)*(-val(element)) else val(element)=-b1(x,y,z)-a1(x,y,z) val(element) = val(element)/(deltah*& & deltah) icol(element) = (ix-2)*idim*idim+(iy-1)*idim+(iz) irow(element) = glob_row element = element+1 endif ! term depending on (x,y-1,z) if (iy == 1) then val(element)=-b2(x,y,z)-a2(x,y,z) val(element) = val(element)/(deltah*& & deltah) zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b2(x,y,z)-a2(x,y,z) val(element) = val(element)/(deltah*deltah) icol(element) = (ix-1)*idim*idim+(iy-2)*idim+(iz) irow(element) = glob_row element = element+1 endif ! term depending on (x,y,z-1) if (iz == 1) then val(element)=-b3(x,y,z)-a3(x,y,z) val(element) = val(element)/(deltah*deltah) zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b3(x,y,z)-a3(x,y,z) val(element) = val(element)/(deltah*deltah) icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz-1) irow(element) = glob_row element = element+1 endif ! term depending on (x,y,z) val(element)=2*b1(x,y,z) + 2*b2(x,y,z)& & + 2*b3(x,y,z) + a1(x,y,z)& & + a2(x,y,z) + a3(x,y,z) val(element) = val(element)/(deltah*deltah) icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz) irow(element) = glob_row element = element+1 ! term depending on (x,y,z+1) if (iz == idim) then val(element)=-b1(x,y,z) val(element) = val(element)/(deltah*deltah) zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b1(x,y,z) val(element) = val(element)/(deltah*deltah) icol(element) = (ix-1)*idim*idim+(iy-1)*idim+(iz+1) irow(element) = glob_row element = element+1 endif ! term depending on (x,y+1,z) if (iy == idim) then val(element)=-b2(x,y,z) val(element) = val(element)/(deltah*deltah) zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b2(x,y,z) val(element) = val(element)/(deltah*deltah) icol(element) = (ix-1)*idim*idim+(iy)*idim+(iz) irow(element) = glob_row element = element+1 endif ! term depending on (x+1,y,z) if (ix