!!$ !!$ Parallel Sparse BLAS version 3.0 !!$ (C) Copyright 2006, 2007, 2008, 2009, 2010, 2012 !!$ 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: spde2d.f90 ! ! Program: spde2d ! This sample program solves a linear system obtained by discretizing a ! PDE with Dirichlet BCs. ! ! ! The PDE is a general second order equation in 2d ! ! a1 dd(u) a2 dd(u) b1 d(u) b2 d(u) ! - ------ - ------ ----- + ------ + c u = f ! dxdx dydy dx dy ! ! with Dirichlet boundary conditions ! u = g ! ! on the unit square 0<=x,y<=1. ! ! ! Note that if b1=b2=c=0., the PDE is the Laplace equation. ! ! 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. ! module spde2d_mod contains ! ! functions parametrizing the differential equation ! function b1(x,y) use psb_base_mod, only : psb_spk_ real(psb_spk_) :: b1 real(psb_spk_), intent(in) :: x,y b1=1.e0/sqrt(2.e0) end function b1 function b2(x,y) use psb_base_mod, only : psb_spk_ real(psb_spk_) :: b2 real(psb_spk_), intent(in) :: x,y b2=1.e0/sqrt(2.e0) end function b2 function c(x,y) use psb_base_mod, only : psb_spk_ real(psb_spk_) :: c real(psb_spk_), intent(in) :: x,y c=0.e0 end function c function a1(x,y) use psb_base_mod, only : psb_spk_ real(psb_spk_) :: a1 real(psb_spk_), intent(in) :: x,y a1=1.e0/80 end function a1 function a2(x,y) use psb_base_mod, only : psb_spk_ real(psb_spk_) :: a2 real(psb_spk_), intent(in) :: x,y a2=1.e0/80 end function a2 function g(x,y) use psb_base_mod, only : psb_spk_, sone, szero real(psb_spk_) :: g real(psb_spk_), intent(in) :: x,y g = szero if (x == sone) then g = sone else if (x == szero) then g = exp(-y**2) end if end function g end module spde2d_mod program spde2d use psb_base_mod use psb_prec_mod use psb_krylov_mod use psb_util_mod use spde2d_mod implicit none ! input parameters character(len=20) :: kmethd, ptype character(len=5) :: afmt integer(psb_ipk_) :: idim ! miscellaneous real(psb_spk_), parameter :: one = 1.e0 real(psb_dpk_) :: t1, t2, tprec ! sparse matrix and preconditioner type(psb_sspmat_type) :: a type(psb_sprec_type) :: prec ! descriptor type(psb_desc_type) :: desc_a ! dense vectors type(psb_s_vect_type) :: xxv,bv ! parallel environment integer(psb_ipk_) :: ictxt, iam, np ! solver parameters integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst integer(psb_long_int_k_) :: amatsize, precsize, descsize, d2size real(psb_spk_) :: err, eps ! 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='pde2d90' 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,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 psb_gen_pde2d(ictxt,idim,a,bv,xxv,desc_a,afmt,a1,a2,b1,b2,c,g,info) call psb_barrier(ictxt) t2 = psb_wtime() - t1 if(info /= psb_success_) then info=psb_err_from_subroutine_ ch_err='psb_gen_pde2d' 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,bv,xxv,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 = a%sizeof() descsize = desc_a%sizeof() precsize = prec%sizeof() 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 system : ",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() end if ! ! 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_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(psb_ipk_) :: ictxt character(len=*) :: kmethd, ptype, afmt integer(psb_ipk_) :: idim, istopc,itmax,itrace,irst integer(psb_ipk_) :: np, iam integer(psb_ipk_) :: 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 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 write(psb_out_unit,'("Solving matrix : ell1")') write(psb_out_unit,'("Grid dimensions : ",i5," x ",i5)')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(izero) call psb_abort(ictxt) stop 1 endif end if ! broadcast parameters to all processors call psb_bcast(ictxt,kmethd) call psb_bcast(ictxt,afmt) call psb_bcast(ictxt,ptype) call psb_bcast(ictxt,idim) call psb_bcast(ictxt,istopc) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,itrace) call psb_bcast(ictxt,irst) 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: pde2d90 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 end program spde2d