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573 lines
18 KiB
Fortran
573 lines
18 KiB
Fortran
!
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!
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! AMG4PSBLAS version 1.0
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! Algebraic Multigrid Package
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! based on PSBLAS (Parallel Sparse BLAS version 3.7)
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!
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! (C) Copyright 2021
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!
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! Salvatore Filippone
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! Pasqua D'Ambra
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! Fabio Durastante
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!
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! Redistribution and use in source and binary forms, with or without
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! modification, are permitted provided that the following conditions
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! are met:
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! 1. Redistributions of source code must retain the above copyright
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! notice, this list of conditions and the following disclaimer.
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! 2. Redistributions in binary form must reproduce the above copyright
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! notice, this list of conditions, and the following disclaimer in the
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! documentation and/or other materials provided with the distribution.
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! 3. The name of the AMG4PSBLAS group or the names of its contributors may
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! not be used to endorse or promote products derived from this
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! software without specific written permission.
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!
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! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AMG4PSBLAS GROUP OR ITS CONTRIBUTORS
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! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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! POSSIBILITY OF SUCH DAMAGE.
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!
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module amg_s_pde_mod
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use psb_base_mod, only : psb_spk_, psb_ipk_, psb_desc_type,&
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& psb_sspmat_type, psb_s_vect_type, szero, sone,&
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& psb_s_base_sparse_mat, psb_s_base_vect_type, psb_i_base_vect_type
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interface
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function s_func_3d(x,y,z) result(val)
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import :: psb_spk_
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real(psb_spk_), intent(in) :: x,y,z
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real(psb_spk_) :: val
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end function s_func_3d
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end interface
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interface amg_gen_pde3d
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module procedure amg_s_gen_pde3d
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end interface amg_gen_pde3d
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contains
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function s_null_func_3d(x,y,z) result(val)
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real(psb_spk_), intent(in) :: x,y,z
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real(psb_spk_) :: val
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val = szero
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end function s_null_func_3d
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!
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! subroutine to allocate and fill in the coefficient matrix and
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! the rhs.
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!
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subroutine amg_s_gen_pde3d(ctxt,idim,a,bv,xv,desc_a,afmt,&
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& a1,a2,a3,b1,b2,b3,c,g,info,f,amold,vmold,imold,partition,nrl,iv)
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use psb_base_mod
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use psb_util_mod
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!
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! Discretizes the partial differential equation
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!
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! a1 dd(u) a2 dd(u) a3 dd(u) b1 d(u) b2 d(u) b3 d(u)
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! - ------ - ------ - ------ + ----- + ------ + ------ + c u = f
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! dxdx dydy dzdz dx dy dz
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!
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! with Dirichlet boundary conditions
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! u = g
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!
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! on the unit cube 0<=x,y,z<=1.
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!
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!
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! Note that if b1=b2=b3=c=0., the PDE is the Laplace equation.
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!
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implicit none
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procedure(s_func_3d) :: b1,b2,b3,c,a1,a2,a3,g
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integer(psb_ipk_) :: idim
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type(psb_sspmat_type) :: a
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type(psb_s_vect_type) :: xv,bv
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type(psb_desc_type) :: desc_a
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integer(psb_ipk_) :: info
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type(psb_ctxt_type) :: ctxt
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character :: afmt*5
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procedure(s_func_3d), optional :: f
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class(psb_s_base_sparse_mat), optional :: amold
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class(psb_s_base_vect_type), optional :: vmold
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class(psb_i_base_vect_type), optional :: imold
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integer(psb_ipk_), optional :: partition, nrl,iv(:)
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! Local variables.
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integer(psb_ipk_), parameter :: nb=20
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type(psb_s_csc_sparse_mat) :: acsc
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type(psb_s_coo_sparse_mat) :: acoo
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type(psb_s_csr_sparse_mat) :: acsr
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real(psb_spk_) :: zt(nb),x,y,z,xph,xmh,yph,ymh,zph,zmh
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integer(psb_ipk_) :: nnz,nr,nlr,i,j,ii,ib,k, partition_
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integer(psb_lpk_) :: m,n,glob_row,nt
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integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner
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! For 3D partition
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! Note: integer control variables going directly into an MPI call
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! must be 4 bytes, i.e. psb_mpk_
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integer(psb_mpk_) :: npdims(3), npp, minfo
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integer(psb_ipk_) :: npx,npy,npz, iamx,iamy,iamz,mynx,myny,mynz
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integer(psb_ipk_), allocatable :: bndx(:),bndy(:),bndz(:)
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! Process grid
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integer(psb_ipk_) :: np, iam
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integer(psb_ipk_) :: icoeff
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integer(psb_lpk_), allocatable :: irow(:),icol(:),myidx(:)
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real(psb_spk_), allocatable :: val(:)
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! deltah dimension of each grid cell
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! deltat discretization time
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real(psb_spk_) :: deltah, sqdeltah, deltah2
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real(psb_spk_), parameter :: rhs=szero,one=sone,zero=szero
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real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb
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integer(psb_ipk_) :: err_act
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procedure(s_func_3d), pointer :: f_
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character(len=20) :: name, ch_err,tmpfmt
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info = psb_success_
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name = 'create_matrix'
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call psb_erractionsave(err_act)
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call psb_info(ctxt, iam, np)
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if (present(f)) then
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f_ => f
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else
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f_ => s_null_func_3d
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end if
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deltah = 1.d0/(idim+1)
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sqdeltah = deltah*deltah
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deltah2 = 2.0_psb_spk_* deltah
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if (present(partition)) then
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if ((1<= partition).and.(partition <= 3)) then
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partition_ = partition
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else
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write(*,*) 'Invalid partition choice ',partition,' defaulting to 3'
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partition_ = 3
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end if
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else
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partition_ = 3
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end if
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! initialize array descriptor and sparse matrix storage. provide an
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! estimate of the number of non zeroes
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m = (1_psb_lpk_*idim)*idim*idim
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n = m
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nnz = 7*((n+np-1)/np)
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if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
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select case(partition_)
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case(1)
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! A BLOCK partition
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if (present(nrl)) then
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nr = nrl
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else
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!
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! Using a simple BLOCK distribution.
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!
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nt = (m+np-1)/np
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nr = max(0,min(nt,m-(iam*nt)))
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end if
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nt = nr
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call psb_sum(ctxt,nt)
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if (nt /= m) then
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write(psb_err_unit,*) iam, 'Initialization error ',nr,nt,m
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info = -1
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call psb_barrier(ctxt)
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call psb_abort(ctxt)
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return
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end if
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!
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! First example of use of CDALL: specify for each process a number of
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! contiguous rows
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!
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call psb_cdall(ctxt,desc_a,info,nl=nr)
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myidx = desc_a%get_global_indices()
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nlr = size(myidx)
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case(2)
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! A partition defined by the user through IV
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if (present(iv)) then
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if (size(iv) /= m) then
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write(psb_err_unit,*) iam, 'Initialization error: wrong IV size',size(iv),m
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info = -1
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call psb_barrier(ctxt)
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call psb_abort(ctxt)
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return
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end if
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else
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write(psb_err_unit,*) iam, 'Initialization error: IV not present'
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info = -1
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call psb_barrier(ctxt)
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call psb_abort(ctxt)
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return
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end if
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!
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! Second example of use of CDALL: specify for each row the
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! process that owns it
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!
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call psb_cdall(ctxt,desc_a,info,vg=iv)
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myidx = desc_a%get_global_indices()
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nlr = size(myidx)
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case(3)
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! A 3-dimensional partition
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! A nifty MPI function will split the process list
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npdims = 0
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call mpi_dims_create(np,3,npdims,info)
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npx = npdims(1)
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npy = npdims(2)
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npz = npdims(3)
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allocate(bndx(0:npx),bndy(0:npy),bndz(0:npz))
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! We can reuse idx2ijk for process indices as well.
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call idx2ijk(iamx,iamy,iamz,iam,npx,npy,npz,base=0)
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! Now let's split the 3D cube in hexahedra
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call dist1Didx(bndx,idim,npx)
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mynx = bndx(iamx+1)-bndx(iamx)
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call dist1Didx(bndy,idim,npy)
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myny = bndy(iamy+1)-bndy(iamy)
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call dist1Didx(bndz,idim,npz)
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mynz = bndz(iamz+1)-bndz(iamz)
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! How many indices do I own?
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nlr = mynx*myny*mynz
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allocate(myidx(nlr))
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! Now, let's generate the list of indices I own
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nr = 0
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do i=bndx(iamx),bndx(iamx+1)-1
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do j=bndy(iamy),bndy(iamy+1)-1
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do k=bndz(iamz),bndz(iamz+1)-1
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nr = nr + 1
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call ijk2idx(myidx(nr),i,j,k,idim,idim,idim)
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end do
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end do
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end do
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if (nr /= nlr) then
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write(psb_err_unit,*) iam,iamx,iamy,iamz, 'Initialization error: NR vs NLR ',&
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& nr,nlr,mynx,myny,mynz
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info = -1
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call psb_barrier(ctxt)
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call psb_abort(ctxt)
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end if
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!
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! Third example of use of CDALL: specify for each process
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! the set of global indices it owns.
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!
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call psb_cdall(ctxt,desc_a,info,vl=myidx)
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!
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! Specify process topology
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!
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block
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!
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! Use adjcncy methods
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!
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integer(psb_mpk_), allocatable :: neighbours(:)
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integer(psb_mpk_) :: cnt
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logical, parameter :: debug_adj=.true.
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if (debug_adj.and.(np > 1)) then
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cnt = 0
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allocate(neighbours(np))
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if (iamx < npx-1) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx+1,iamy,iamz,npx,npy,npz,base=0)
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end if
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if (iamy < npy-1) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx,iamy+1,iamz,npx,npy,npz,base=0)
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end if
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if (iamz < npz-1) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx,iamy,iamz+1,npx,npy,npz,base=0)
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end if
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if (iamx >0) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx-1,iamy,iamz,npx,npy,npz,base=0)
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end if
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if (iamy >0) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx,iamy-1,iamz,npx,npy,npz,base=0)
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end if
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if (iamz >0) then
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cnt = cnt + 1
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call ijk2idx(neighbours(cnt),iamx,iamy,iamz-1,npx,npy,npz,base=0)
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end if
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call psb_realloc(cnt, neighbours,info)
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call desc_a%set_p_adjcncy(neighbours)
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!write(0,*) iam,' Check on neighbours: ',desc_a%get_p_adjcncy()
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end if
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end block
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case default
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write(psb_err_unit,*) iam, 'Initialization error: should not get here'
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info = -1
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call psb_barrier(ctxt)
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call psb_abort(ctxt)
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return
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end select
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if (info == psb_success_) call psb_spall(a,desc_a,info,nnz=nnz)
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! define rhs from boundary conditions; also build initial guess
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if (info == psb_success_) call psb_geall(xv,desc_a,info)
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if (info == psb_success_) call psb_geall(bv,desc_a,info)
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call psb_barrier(ctxt)
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talc = psb_wtime()-t0
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='allocation rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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! we build an auxiliary matrix consisting of one row at a
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! time; just a small matrix. might be extended to generate
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! a bunch of rows per call.
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!
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allocate(val(20*nb),irow(20*nb),&
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&icol(20*nb),stat=info)
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if (info /= psb_success_ ) then
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info=psb_err_alloc_dealloc_
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call psb_errpush(info,name)
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goto 9999
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endif
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! loop over rows belonging to current process in a block
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! distribution.
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call psb_barrier(ctxt)
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t1 = psb_wtime()
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do ii=1, nlr,nb
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ib = min(nb,nlr-ii+1)
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icoeff = 1
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do k=1,ib
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i=ii+k-1
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! local matrix pointer
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glob_row=myidx(i)
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! compute gridpoint coordinates
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call idx2ijk(ix,iy,iz,glob_row,idim,idim,idim)
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! x, y, z coordinates
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x = (ix-1)*deltah
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y = (iy-1)*deltah
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z = (iz-1)*deltah
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zt(k) = f_(x,y,z)
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! internal point: build discretization
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!
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! term depending on (x-1,y,z)
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!
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val(icoeff) = -a1(x,y,z)/sqdeltah-b1(x,y,z)/deltah2
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if (ix == 1) then
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zt(k) = g(szero,y,z)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix-1,iy,iz,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y-1,z)
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val(icoeff) = -a2(x,y,z)/sqdeltah-b2(x,y,z)/deltah2
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if (iy == 1) then
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zt(k) = g(x,szero,z)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix,iy-1,iz,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y,z-1)
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val(icoeff)=-a3(x,y,z)/sqdeltah-b3(x,y,z)/deltah2
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if (iz == 1) then
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zt(k) = g(x,y,szero)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix,iy,iz-1,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y,z)
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val(icoeff)=(2*sone)*(a1(x,y,z)+a2(x,y,z)+a3(x,y,z))/sqdeltah &
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& + c(x,y,z)
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call ijk2idx(icol(icoeff),ix,iy,iz,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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! term depending on (x,y,z+1)
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val(icoeff)=-a3(x,y,z)/sqdeltah+b3(x,y,z)/deltah2
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if (iz == idim) then
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zt(k) = g(x,y,sone)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix,iy,iz+1,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x,y+1,z)
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val(icoeff)=-a2(x,y,z)/sqdeltah+b2(x,y,z)/deltah2
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if (iy == idim) then
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zt(k) = g(x,sone,z)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix,iy+1,iz,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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! term depending on (x+1,y,z)
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val(icoeff)=-a1(x,y,z)/sqdeltah+b1(x,y,z)/deltah2
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if (ix==idim) then
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zt(k) = g(sone,y,z)*(-val(icoeff)) + zt(k)
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else
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call ijk2idx(icol(icoeff),ix+1,iy,iz,idim,idim,idim)
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irow(icoeff) = glob_row
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icoeff = icoeff+1
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endif
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end do
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call psb_spins(icoeff-1,irow,icol,val,a,desc_a,info)
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if(info /= psb_success_) exit
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call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),bv,desc_a,info)
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if(info /= psb_success_) exit
|
|
zt(:)=szero
|
|
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)
|
|
else
|
|
call psb_spasb(a,desc_a,info,afmt=afmt)
|
|
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 amg_s_gen_pde3d
|
|
|
|
!
|
|
! functions parametrizing the differential equation
|
|
!
|
|
function b1(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: b1
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
b1=szero
|
|
end function b1
|
|
function b2(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: b2
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
b2=szero
|
|
end function b2
|
|
function b3(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: b3
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
b3=szero
|
|
end function b3
|
|
function c(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: c
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
c=szero
|
|
end function c
|
|
function a1(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: a1
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
a1=sone
|
|
end function a1
|
|
function a2(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: a2
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
a2=sone
|
|
end function a2
|
|
function a3(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone
|
|
real(psb_spk_) :: a3
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
a3=sone
|
|
end function a3
|
|
function g(x,y,z)
|
|
use psb_base_mod, only : psb_spk_, sone, szero
|
|
real(psb_spk_) :: g
|
|
real(psb_spk_), intent(in) :: x,y,z
|
|
g = szero
|
|
if (x == sone) then
|
|
g = sone
|
|
else if (x == szero) then
|
|
g = exp(y**2-z**2)
|
|
end if
|
|
end function g
|
|
end module amg_s_pde_mod
|
|
|