!
!
! AMG4PSBLAS version 1.0
! Algebraic Multigrid Package
! based on PSBLAS (Parallel Sparse BLAS version 3.7)
!
! (C) Copyright 2021
!
! Salvatore Filippone
! Pasqua D'Ambra
! Fabio Durastante
!
! 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 AMG4PSBLAS 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 AMG4PSBLAS 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.
!
module amg_s_pde_mod
use psb_base_mod, only : psb_spk_, psb_ipk_, psb_desc_type,&
& psb_sspmat_type, psb_s_vect_type, szero, sone,&
& psb_s_base_sparse_mat, psb_s_base_vect_type, psb_i_base_vect_type
interface
function s_func_3d(x,y,z) result(val)
import :: psb_spk_
real(psb_spk_), intent(in) :: x,y,z
real(psb_spk_) :: val
end function s_func_3d
end interface
interface amg_gen_pde3d
module procedure amg_s_gen_pde3d
end interface amg_gen_pde3d
contains
function s_null_func_3d(x,y,z) result(val)
real(psb_spk_), intent(in) :: x,y,z
real(psb_spk_) :: val
val = szero
end function s_null_func_3d
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs.
!
subroutine amg_s_gen_pde3d(ctxt,idim,a,bv,xv,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info,f,amold,vmold,imold,partition,nrl,iv)
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
procedure(s_func_3d) :: b1,b2,b3,c,a1,a2,a3,g
integer(psb_ipk_) :: idim
type(psb_sspmat_type) :: a
type(psb_s_vect_type) :: xv,bv
type(psb_desc_type) :: desc_a
integer(psb_ipk_) :: info
type(psb_ctxt_type) :: ctxt
character :: afmt*5
procedure(s_func_3d), optional :: f
class(psb_s_base_sparse_mat), optional :: amold
class(psb_s_base_vect_type), optional :: vmold
class(psb_i_base_vect_type), optional :: imold
integer(psb_ipk_), optional :: partition, nrl,iv(:)
! Local variables.
integer(psb_ipk_), parameter :: nb=20
type(psb_s_csc_sparse_mat) :: acsc
type(psb_s_coo_sparse_mat) :: acoo
type(psb_s_csr_sparse_mat) :: acsr
real(psb_spk_) :: zt(nb),x,y,z,xph,xmh,yph,ymh,zph,zmh
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_spk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_spk_) :: deltah, sqdeltah, deltah2
real(psb_spk_), parameter :: rhs=szero,one=sone,zero=szero
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen, tcdasb
integer(psb_ipk_) :: err_act
procedure(s_func_3d), pointer :: f_
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_ => s_null_func_3d
end if
deltah = 1.d0/(idim+1)
sqdeltah = deltah*deltah
deltah2 = 2.0_psb_spk_* 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 = 7*((n+np-1)/np)
if(iam == psb_root_) write(psb_out_unit,'("Generating Matrix (size=",i0,")...")')n
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)
!
! Specify process topology
!
block
!
! Use adjcncy methods
!
integer(psb_mpk_), allocatable :: neighbours(:)
integer(psb_mpk_) :: cnt
logical, parameter :: debug_adj=.true.
if (debug_adj.and.(np > 1)) then
cnt = 0
allocate(neighbours(np))
if (iamx < npx-1) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx+1,iamy,iamz,npx,npy,npz,base=0)
end if
if (iamy < npy-1) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx,iamy+1,iamz,npx,npy,npz,base=0)
end if
if (iamz < npz-1) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx,iamy,iamz+1,npx,npy,npz,base=0)
end if
if (iamx >0) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx-1,iamy,iamz,npx,npy,npz,base=0)
end if
if (iamy >0) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx,iamy-1,iamz,npx,npy,npz,base=0)
end if
if (iamz >0) then
cnt = cnt + 1
call ijk2idx(neighbours(cnt),iamx,iamy,iamz-1,npx,npy,npz,base=0)
end if
call psb_realloc(cnt, neighbours,info)
call desc_a%set_p_adjcncy(neighbours)
!write(0,*) iam,' Check on neighbours: ',desc_a%get_p_adjcncy()
end if
end block
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)
! 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(szero,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,szero,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,szero)*(-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*sone)*(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,sone)*(-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,sone,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(sone,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(:)=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