!!$ !!$ 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. 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. !!$ !!$ ! 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 pdgen use psb_base_mod use psb_util_mod implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer(psb_ipk_) :: idim ! miscellaneous real(psb_dpk_), parameter :: one = 1.d0 real(psb_dpk_) :: t1, t2, tprec, flops, tflops, tt1, tt2, bdwdth ! sparse matrix and preconditioner type(psb_dspmat_type) :: a ! descriptor type(psb_desc_type) :: desc_a, desc_b ! dense matrices type(psb_d_vect_type) :: xxv,bv, vtst real(psb_dpk_), allocatable :: tst(:) ! blacs parameters integer(psb_ipk_) :: ictxt, iam, np ! solver parameters integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nr integer(psb_long_int_k_) :: amatsize, precsize, descsize, d2size, annz, nbytes real(psb_dpk_) :: err, eps integer(psb_ipk_), parameter :: times=10 ! other variables integer(psb_ipk_) :: info, i character(len=20) :: name,ch_err character(len=40) :: fname 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(itwo) ! ! Hello world ! if (iam == psb_root_) then write(*,*) 'Welcome to PSBLAS version: ',psb_version_string_ write(*,*) 'This is the ',trim(name),' sample program' end if ! ! get parameters ! call get_parms(ictxt,afmt,idim) ! ! allocate and fill in the coefficient matrix, rhs and initial guess ! call psb_barrier(ictxt) t1 = psb_wtime() call create_matrix(idim,a,bv,xxv,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,'(" ")') !!$ write(fname,'(a,i0,a)') 'pde-',idim,'.hb' !!$ call hb_write(a,info,filename=fname,rhs=b,key='PDEGEN',mtitle='MLD2P4 pdegen Test matrix ') !!$ write(fname,'(a,i2.2,a,i2.2,a)') 'amat-',iam,'-',np,'.mtx' !!$ call a%print(fname) !!$ call psb_cdprt(20+iam,desc_a,short=.false.) !!$ call psb_cdcpy(desc_a,desc_b,info) !!$ call psb_set_debug_level(9999) call psb_cdbldext(a,desc_a,itwo,desc_b,info,extype=psb_ovt_asov_) if (info /= 0) then write(0,*) 'Error from bldext' call psb_abort(ictxt) end if call xxv%set(done) call psb_barrier(ictxt) t1 = psb_wtime() do i=1,times call psb_spmm(done,a,xxv,dzero,bv,desc_a,info,'n') end do call psb_barrier(ictxt) t2 = psb_wtime() - t1 call psb_amx(ictxt,t2) ! FIXME: cache flush needed here call psb_barrier(ictxt) tt1 = psb_wtime() do i=1,times call psb_spmm(done,a,xxv,dzero,bv,desc_a,info,'t') end do call psb_barrier(ictxt) tt2 = psb_wtime() - tt1 call psb_amx(ictxt,tt2) call psb_amx(ictxt,t2) nr = desc_a%get_global_rows() annz = a%get_nzeros() amatsize = a%sizeof() descsize = psb_sizeof(desc_a) call psb_sum(ictxt,annz) call psb_sum(ictxt,amatsize) call psb_sum(ictxt,descsize) if (iam == psb_root_) then flops = 1.d1*2*annz tflops=flops write(psb_out_unit,'("Matrix: ell1 ",i0)') idim write(psb_out_unit,'("Test on : ",i20," processors")') np write(psb_out_unit,'("Size of matrix : ",i20," ")') nr write(psb_out_unit,'("Number of nonzeros : ",i20," ")') annz write(psb_out_unit,'("Memory occupation : ",i20," ")') amatsize write(psb_out_unit,'("Number of flops (",i0," prod) : ",F20.0," ")') times,flops flops = flops / (t2) tflops = tflops / (tt2) write(psb_out_unit,'("Time for ",i0," products (s) : ",F20.3)')times, t2 write(psb_out_unit,'("Time per product (ms) : ",F20.3)') t2*1.d3/(1.d0*times) write(psb_out_unit,'("MFLOPS : ",F20.3)') flops/1.d6 write(psb_out_unit,'("Time for ",i0," products (s) (trans.): ",F20.3)') times,tt2 write(psb_out_unit,'("Time per product (ms) (trans.): ",F20.3)') tt2*1.d3/(1.d0*times) write(psb_out_unit,'("MFLOPS (trans.): ",F20.3)') tflops/1.d6 ! ! This computation is valid for CSR ! nbytes = nr*(2*psb_sizeof_dp + psb_sizeof_int)+& & annz*(psb_sizeof_dp + psb_sizeof_int) bdwdth = times*nbytes/(t2*1.d6) write(psb_out_unit,*) write(psb_out_unit,'("MBYTES/S : ",F20.3)') bdwdth bdwdth = times*nbytes/(tt2*1.d6) write(psb_out_unit,'("MBYTES/S (trans): ",F20.3)') bdwdth write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt() write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt() write(psb_out_unit,'("Storage type for DESC_B: ",a)') desc_b%indxmap%get_fmt() end if !!$ 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 PREC: ",i12)')precsize !!$ write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize !!$ write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt() !!$ write(psb_out_unit,'("Storage type for DESC_B: ",a)') desc_b%indxmap%get_fmt() ! ! cleanup storage and exit ! call psb_gefree(bv,desc_a,info) call psb_gefree(xxv,desc_a,info) call psb_spfree(a,desc_a,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,afmt,idim) integer(psb_ipk_) :: ictxt character(len=*) :: afmt integer(psb_ipk_) :: idim integer(psb_ipk_) :: np, iam integer(psb_ipk_) :: intbuf(10), ip call psb_info(ictxt, iam, np) if (iam == 0) then read(psb_inp_unit,*) afmt read(psb_inp_unit,*) idim endif call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,idim) if (iam == 0) then write(psb_out_unit,'("Testing 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,'(" ")') end if return end subroutine get_parms ! ! print an error message ! subroutine pr_usage(iout) integer(psb_ipk_) :: 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,bv,xxv,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_base_mod use psb_mat_mod implicit none integer(psb_ipk_) :: idim integer(psb_ipk_), parameter :: nb=20 type(psb_d_vect_type) :: xxv,bv type(psb_desc_type) :: desc_a integer(psb_ipk_) :: ictxt, info character :: afmt*5 type(psb_dspmat_type) :: 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(psb_ipk_) :: m,n,nnz,glob_row,nlr,i,ii,ib,k integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner integer(psb_ipk_) :: np, iam, nr, nt integer(psb_ipk_) :: element integer(psb_ipk_), allocatable :: irow(:),icol(:),myidx(:) real(psb_dpk_), allocatable :: val(:) ! deltah dimension of each grid cell ! deltat discretization time real(psb_dpk_) :: deltah, deltah2 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(psb_ipk_) :: 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) deltah2 = deltah*deltah ! 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(xxv,desc_a,info) if (info == psb_success_) call psb_geall(bv,desc_a,info) nlr = desc_a%get_local_rows() 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)/deltah2-a1(x,y,z)/deltah zt(k) = exp(-x**2-y**2-z**2)*(-val(element)) else val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/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)/deltah2-a2(x,y,z)/deltah zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element)) else val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/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)/deltah2-a3(x,y,z)/deltah zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/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))/deltah2& & + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/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)/deltah2 zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b1(x,y,z)/deltah2 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)/deltah2 zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b2(x,y,z)/deltah2 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==idim) then val(element)=-b3(x,y,z)/deltah2 zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element)) else val(element)=-b3(x,y,z)/deltah2 icol(element) = (ix)*idim*idim+(iy-1)*idim+(iz) irow(element) = glob_row element = element+1 endif end do call psb_spins(element-1,irow,icol,val,a,desc_a,info) if(info /= psb_success_) exit call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),bv,desc_a,info) if(info /= psb_success_) exit zt(:)=0.d0 call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xxv,desc_a,info) if(info /= psb_success_) exit end do tgen = psb_wtime()-t1 if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='insert rout.' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if deallocate(val,irow,icol) call psb_barrier(ictxt) t1 = psb_wtime() call psb_cdasb(desc_a,info) if (info == psb_success_) & & call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt) call psb_barrier(ictxt) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='asb rout.' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if if (info == psb_success_) call psb_geasb(xxv,desc_a,info) if (info == psb_success_) call psb_geasb(bv,desc_a,info) if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='asb rout.' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if tasb = psb_wtime()-t1 call psb_barrier(ictxt) ttot = psb_wtime() - t0 call psb_amx(ictxt,talc) call psb_amx(ictxt,tgen) call psb_amx(ictxt,tasb) call psb_amx(ictxt,ttot) if(iam == psb_root_) then tmpfmt = a%get_fmt() write(psb_out_unit,'("The matrix has been generated and assembled in ",a3," format.")')& & tmpfmt write(psb_out_unit,'("-allocation time : ",es12.5)') talc write(psb_out_unit,'("-coeff. gen. time : ",es12.5)') tgen write(psb_out_unit,'("-assembly time : ",es12.5)') tasb write(psb_out_unit,'("-total time : ",es12.5)') ttot end if call psb_erractionrestore(err_act) return 9999 continue call psb_erractionrestore(err_act) if (err_act == psb_act_abort_) then call psb_error(ictxt) return end if return end subroutine create_matrix end program pdgen ! ! functions parametrizing the differential equation ! function a1(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a1 real(psb_dpk_) :: x,y,z a1=1.d0 end function a1 function a2(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a2 real(psb_dpk_) :: x,y,z a2=2.d1*y end function a2 function a3(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a3 real(psb_dpk_) :: x,y,z a3=1.d0 end function a3 function a4(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: a4 real(psb_dpk_) :: x,y,z a4=1.d0 end function a4 function b1(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b1 real(psb_dpk_) :: x,y,z b1=1.d0 end function b1 function b2(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b2 real(psb_dpk_) :: x,y,z b2=1.d0 end function b2 function b3(x,y,z) use psb_base_mod, only : psb_dpk_ real(psb_dpk_) :: b3 real(psb_dpk_) :: x,y,z b3=1.d0 end function b3