module psb_d_pde3d_mod use psb_base_mod, only : psb_dpk_, psb_ipk_, psb_lpk_, psb_desc_type,& & psb_dspmat_type, psb_d_vect_type, dzero,& & psb_d_base_sparse_mat, psb_d_base_vect_type, & & psb_i_base_vect_type, psb_l_base_vect_type interface function d_func_3d(x,y,z) result(val) import :: psb_dpk_ real(psb_dpk_), intent(in) :: x,y,z real(psb_dpk_) :: val end function d_func_3d end interface interface psb_gen_pde3d module procedure psb_d_gen_pde3d end interface psb_gen_pde3d contains function d_null_func_3d(x,y,z) result(val) real(psb_dpk_), intent(in) :: x,y,z real(psb_dpk_) :: val val = dzero end function d_null_func_3d ! ! functions parametrizing the differential equation ! ! ! Note: b1, b2 and b3 are the coefficients of the first ! derivative of the unknown function. The default ! we apply here is to have them zero, so that the resulting ! matrix is symmetric/hermitian and suitable for ! testing with CG and FCG. ! When testing methods for non-hermitian matrices you can ! change the B1/B2/B3 functions to e.g. done/sqrt((3*done)) ! function b1(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b1 real(psb_dpk_), intent(in) :: x,y,z b1=done/sqrt((3*done)) end function b1 function b2(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b2 real(psb_dpk_), intent(in) :: x,y,z b2=done/sqrt((3*done)) end function b2 function b3(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: b3 real(psb_dpk_), intent(in) :: x,y,z b3=done/sqrt((3*done)) end function b3 function c(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: c real(psb_dpk_), intent(in) :: x,y,z c=dzero end function c function a1(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a1 real(psb_dpk_), intent(in) :: x,y,z a1=done/80 end function a1 function a2(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a2 real(psb_dpk_), intent(in) :: x,y,z a2=done/80 end function a2 function a3(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: a3 real(psb_dpk_), intent(in) :: x,y,z a3=done/80 end function a3 function g(x,y,z) use psb_base_mod, only : psb_dpk_, done, dzero implicit none real(psb_dpk_) :: g real(psb_dpk_), intent(in) :: x,y,z g = dzero if (x == done) then g = done else if (x == dzero) then g = exp(y**2-z**2) end if end function g ! ! subroutine to allocate and fill in the coefficient matrix and ! the rhs. ! subroutine psb_d_gen_pde3d(ctxt,idim,a,bv,xv,desc_a,afmt,info,& & f,amold,vmold,imold,partition,nrl,iv,tnd) use psb_base_mod use psb_util_mod ! ! Discretizes the partial differential equation ! ! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u) ! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f ! dxdx dydy dzdz dx dy dz ! ! with Dirichlet boundary conditions ! u = g ! ! on the unit cube 0<=x,y,z<=1. ! ! ! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation. ! implicit none integer(psb_ipk_) :: idim type(psb_dspmat_type) :: a type(psb_d_vect_type) :: xv,bv type(psb_desc_type) :: desc_a type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: info character(len=*) :: afmt procedure(d_func_3d), optional :: f class(psb_d_base_sparse_mat), optional :: amold class(psb_d_base_vect_type), optional :: vmold class(psb_i_base_vect_type), optional :: imold integer(psb_ipk_), optional :: partition, nrl,iv(:) logical, optional :: tnd ! Local variables. integer(psb_ipk_), parameter :: nb=20 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_) :: nnz,nr,nlr,i,j,ii,ib,k, partition_ integer(psb_lpk_) :: m,n,glob_row,nt integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner ! For 3D partition ! Note: integer control variables going directly into an MPI call ! must be 4 bytes, i.e. psb_mpk_ integer(psb_mpk_) :: npdims(3), npp, minfo integer(psb_ipk_) :: npx,npy,npz, iamx,iamy,iamz,mynx,myny,mynz integer(psb_ipk_), allocatable :: bndx(:),bndy(:),bndz(:) ! Process grid integer(psb_ipk_) :: np, iam integer(psb_ipk_) :: icoeff integer(psb_lpk_), allocatable :: irow(:),icol(:),myidx(:) real(psb_dpk_), allocatable :: val(:) ! deltah dimension of each grid cell ! deltat discretization time real(psb_dpk_) :: deltah, sqdeltah, deltah2 real(psb_dpk_), parameter :: rhs=dzero,one=done,zero=dzero real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb integer(psb_ipk_) :: err_act procedure(d_func_3d), pointer :: f_ logical :: tnd_ character(len=20) :: name, ch_err,tmpfmt info = psb_success_ name = 'create_matrix' call psb_erractionsave(err_act) call psb_info(ctxt, iam, np) if (present(f)) then f_ => f else f_ => d_null_func_3d end if deltah = done/(idim+2) sqdeltah = deltah*deltah deltah2 = (2*done)* deltah if (present(partition)) then if ((1<= partition).and.(partition <= 3)) then partition_ = partition else write(*,*) 'Invalid partition choice ',partition,' defaulting to 3' partition_ = 3 end if else partition_ = 3 end if ! initialize array descriptor and sparse matrix storage. provide an ! estimate of the number of non zeroes m = (1_psb_lpk_*idim)*idim*idim n = m nnz = ((n*7)/(np)) if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n t0 = psb_wtime() select case(partition_) case(1) ! A BLOCK partition if (present(nrl)) then nr = nrl else ! ! Using a simple BLOCK distribution. ! nt = (m+np-1)/np nr = max(0,min(nt,m-(iam*nt))) end if nt = nr call psb_sum(ctxt,nt) if (nt /= m) then write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m info = -1 call psb_barrier(ctxt) call psb_abort(ctxt) return end if ! ! First example of use of CDALL: specify for each process a number of ! contiguous rows ! call psb_cdall(ctxt,desc_a,info,nl=nr) myidx = desc_a%get_global_indices() nlr = size(myidx) case(2) ! A partition defined by the user through IV if (present(iv)) then if (size(iv) /= m) then write(psb_err_unit,*) iam, 'Initialization error: wrong IV size',size(iv),m info = -1 call psb_barrier(ctxt) call psb_abort(ctxt) return end if else write(psb_err_unit,*) iam, 'Initialization error: IV not present' info = -1 call psb_barrier(ctxt) call psb_abort(ctxt) return end if ! ! Second example of use of CDALL: specify for each row the ! process that owns it ! call psb_cdall(ctxt,desc_a,info,vg=iv) myidx = desc_a%get_global_indices() nlr = size(myidx) case(3) ! A 3-dimensional partition ! A nifty MPI function will split the process list npdims = 0 call mpi_dims_create(np,3,npdims,info) npx = npdims(1) npy = npdims(2) npz = npdims(3) allocate(bndx(0:npx),bndy(0:npy),bndz(0:npz)) ! We can reuse idx2ijk for process indices as well. call idx2ijk(iamx,iamy,iamz,iam,npx,npy,npz,base=0) ! Now let's split the 3D cube in hexahedra call dist1Didx(bndx,idim,npx) mynx = bndx(iamx+1)-bndx(iamx) call dist1Didx(bndy,idim,npy) myny = bndy(iamy+1)-bndy(iamy) call dist1Didx(bndz,idim,npz) mynz = bndz(iamz+1)-bndz(iamz) ! How many indices do I own? nlr = mynx*myny*mynz allocate(myidx(nlr)) ! Now, let's generate the list of indices I own nr = 0 do i=bndx(iamx),bndx(iamx+1)-1 do j=bndy(iamy),bndy(iamy+1)-1 do k=bndz(iamz),bndz(iamz+1)-1 nr = nr + 1 call ijk2idx(myidx(nr),i,j,k,idim,idim,idim) end do end do end do if (nr /= nlr) then write(psb_err_unit,*) iam,iamx,iamy,iamz, 'Initialization error: NR vs NLR ',& & nr,nlr,mynx,myny,mynz info = -1 call psb_barrier(ctxt) call psb_abort(ctxt) end if ! ! Third example of use of CDALL: specify for each process ! the set of global indices it owns. ! call psb_cdall(ctxt,desc_a,info,vl=myidx) case default write(psb_err_unit,*) iam, 'Initialization error: should not get here' info = -1 call psb_barrier(ctxt) call psb_abort(ctxt) return end select if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz,& & dupl=psb_dupl_err_) ! define rhs from boundary conditions; also build initial guess if (info == psb_success_) call psb_geall(xv,desc_a,info) if (info == psb_success_) call psb_geall(bv,desc_a,info) call psb_barrier(ctxt) 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),stat=info) if (info /= psb_success_ ) then info=psb_err_alloc_dealloc_ call psb_errpush(info,name) goto 9999 endif ! loop over rows belonging to current process in a block ! distribution. call psb_barrier(ctxt) t1 = psb_wtime() do ii=1, nlr,nb ib = min(nb,nlr-ii+1) icoeff = 1 do k=1,ib i=ii+k-1 ! local matrix pointer glob_row=myidx(i) ! compute gridpoint coordinates call idx2ijk(ix,iy,iz,glob_row,idim,idim,idim) ! x, y, z coordinates x = (ix-1)*deltah y = (iy-1)*deltah z = (iz-1)*deltah zt(k) = f_(x,y,z) ! internal point: build discretization ! ! term depending on (x-1,y,z) ! val(icoeff) = -a1(x,y,z)/sqdeltah-b1(x,y,z)/deltah2 if (ix == 1) then zt(k) = g(dzero,y,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix-1,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y-1,z) val(icoeff) = -a2(x,y,z)/sqdeltah-b2(x,y,z)/deltah2 if (iy == 1) then zt(k) = g(x,dzero,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy-1,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y,z-1) val(icoeff)=-a3(x,y,z)/sqdeltah-b3(x,y,z)/deltah2 if (iz == 1) then zt(k) = g(x,y,dzero)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy,iz-1,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y,z) val(icoeff)=(2*done)*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah & & + c(x,y,z) call ijk2idx(icol(icoeff),ix,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 ! term depending on (x,y,z+1) val(icoeff)=-a3(x,y,z)/sqdeltah+b3(x,y,z)/deltah2 if (iz == idim) then zt(k) = g(x,y,done)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy,iz+1,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x,y+1,z) val(icoeff)=-a2(x,y,z)/sqdeltah+b2(x,y,z)/deltah2 if (iy == idim) then zt(k) = g(x,done,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix,iy+1,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif ! term depending on (x+1,y,z) val(icoeff)=-a1(x,y,z)/sqdeltah+b1(x,y,z)/deltah2 if (ix==idim) then zt(k) = g(done,y,z)*(-val(icoeff)) + zt(k) else call ijk2idx(icol(icoeff),ix+1,iy,iz,idim,idim,idim) irow(icoeff) = glob_row icoeff = icoeff+1 endif end do call psb_spins(icoeff-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(:)=dzero call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xv,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(ctxt) t1 = psb_wtime() call psb_cdasb(desc_a,info,mold=imold) tcdasb = psb_wtime()-t1 call psb_barrier(ctxt) t1 = psb_wtime() if (info == psb_success_) then if (present(amold)) then call psb_spasb(a,desc_a,info,mold=amold,bld_and=tnd) else call psb_spasb(a,desc_a,info,afmt=afmt,bld_and=tnd) end if end if call psb_barrier(ctxt) 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(xv,desc_a,info,mold=vmold) if (info == psb_success_) call psb_geasb(bv,desc_a,info,mold=vmold) 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(ctxt) ttot = psb_wtime() - t0 call psb_amx(ctxt,talc) call psb_amx(ctxt,tgen) call psb_amx(ctxt,tasb) call psb_amx(ctxt,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,'("-desc asbly time : ",es12.5)') tcdasb write(psb_out_unit,'("- mat asbly time : ",es12.5)') tasb write(psb_out_unit,'("-total time : ",es12.5)') ttot end if call psb_erractionrestore(err_act) return 9999 call psb_error_handler(ctxt,err_act) return end subroutine psb_d_gen_pde3d end module psb_d_pde3d_mod program test use psb_base_mod use psb_ext_mod use psb_oacc_mod use psb_d_pde3d_mod implicit none integer(psb_ipk_) :: n, i, info, m, nrm, nz integer(psb_ipk_), parameter :: ntests=80, ngpu=20 real(psb_dpk_) :: dot_dev, dot_host type(psb_d_vect_oacc) :: tx, ty type(psb_d_oacc_csr_sparse_mat) :: aacsr real(psb_dpk_) :: t0, t1, t2, t3, csflp, elflp double precision, external :: etime type(psb_dspmat_type) :: a type(psb_desc_type) :: desc_a type(psb_d_vect_type) :: xxv, bv type(psb_d_csr_sparse_mat) :: acsr character(len=5) :: afmt='csr' real(psb_dpk_), allocatable :: vv(:), ydev(:), yhost(:) type(psb_ctxt_type) :: ctxt integer(psb_ipk_) :: iam, np, nth, idim integer(psb_epk_) :: neq call psb_init(ctxt) call psb_info(ctxt, iam, np) write(*,*) 'Enter size :' read(*,*) idim idim = max(1, idim) n = idim**3 call psb_gen_pde3d(ctxt, idim, a, bv, xxv, desc_a, afmt, info) call a%cp_to(acsr) m = acsr%get_nrows() n = acsr%get_ncols() nz = acsr%get_nzeros() call aacsr%all(m, n, nz, info) aacsr%val = (acsr%val) aacsr%ja = (acsr%ja) aacsr%irp = (acsr%irp) call aacsr%set_host() call aacsr%sync() call initialize(n) call to_host() t2 = etime() do i = 1, ntests dot_host = h_dot(n) end do t3 = etime() call tx%all(n, info) call ty%all(n, info) vv = bv%get_vect() call bv%set_vect(v1) call tx%set_vect(v1) call ty%set_vect(v2) t0 = etime() do i = 1, ntests * ngpu dot_dev = tx%dot_v(n, ty) end do !$acc wait t1 = etime() write(*,*) ' Dot Results : dev:', dot_dev, ' host:', dot_host write(*,*) ' Timing : dev:', t1 - t0, (t1 - t0) / (ntests * ngpu), & ' host:', t3 - t2, (t3 - t2) / ntests call a%mv_from(acsr) t2 = etime() do i = 1, ntests call a%spmm(done, bv, dzero, xxv, info) end do t3 = etime() yhost = xxv%get_vect() t0 = etime() do i = 1, ntests * ngpu call aacsr%vect_mv(done, tx, dzero, ty, info) end do !$acc wait t1 = etime() ydev = ty%get_vect() write(*,*) 'Correctness check: ', maxval(abs(ydev(:) - yhost(:))) write(*,*) ' CSR PROD ' write(*, '(2(a,f12.3,2x))') ' Timing (ms): ' csflp = 2.d0 * nz / ((t1 - t0) / (ntests * ngpu)) write(*, '(2(a,f12.3,2x))') ' dev:', 1e3 * (t1 - t0) / (ntests * ngpu), ' :', csflp / 1.d6 csflp = 2.d0 * nz / ((t3 - t2) / (ntests)) write(*, '(2(a,f12.3,2x))') ' host:', 1e3 * (t3 - t2) / ntests, ' :', csflp / 1.d6 write(*,*) 'Done' call tx%free(info) call ty%free(info) call finalize_dev() call finalize_host() call psb_exit(ctxt) end program test