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mld2p4-2:

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tests/pdegen/Makefile
 tests/pdegen/ppde.f90
 tests/pdegen/ppde2d.f90
 tests/pdegen/ppde3d.f90
 tests/pdegen/spde.f90
 tests/pdegen/spde2d.f90
 tests/pdegen/spde3d.f90

Fixed test cases to use new support in psblas.
stopcriterion
Salvatore Filippone 13 years ago
parent cf78bb0c03
commit ad88b4298d
5 changed files with 1077 additions and 712 deletions
Show Stats Download Patch File Download Diff File

29
tests/pdegen/Makefile
Unescape Escape View File

@ -11,25 +11,32 @@ FINCLUDES=$(FMFLAG). $(FMFLAG)$(MLDLIBDIR) $(FMFLAG)$(PSBINCDIR) $(FIFLAG).
EXEDIR=./runs
all: spde ppde
all: spde3d ppde3d spde2d ppde2d
check: all
cd $(EXEDIR) ; ./ppde < ppde.inp
ppde3d: ppde3d.o data_input.o
$(F90LINK) ppde3d.o data_input.o -o ppde3d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv ppde3d $(EXEDIR)
ppde: ppde.o data_input.o
$(F90LINK) ppde.o data_input.o -o ppde $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv ppde $(EXEDIR)
spde3d: spde3d.o data_input.o
$(F90LINK) spde3d.o data_input.o -o spde3d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv spde3d $(EXEDIR)
spde: spde.o data_input.o
$(F90LINK) spde.o data_input.o -o spde $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv spde $(EXEDIR)
ppde2d: ppde2d.o data_input.o
$(F90LINK) ppde2d.o data_input.o -o ppde2d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv ppde2d $(EXEDIR)
ppde.o spde.o: data_input.o
spde2d: spde2d.o data_input.o
$(F90LINK) spde2d.o data_input.o -o spde2d $(MLD_LIB) $(PSBLAS_LIB) $(LDLIBS)
/bin/mv spde2d $(EXEDIR)
ppde3d.o spde3d.o ppde2d.o spde2d.o: data_input.o
clean:
/bin/rm -f data_input.o ppde.o $(EXEDIR)/ppde spde.o $(EXEDIR)/spde
/bin/rm -f data_input.o ppde3d.o spde3d.o ppde2d.o spde2d.o \
$(EXEDIR)/ppde3d $(EXEDIR)/spde3d $(EXEDIR)/ppde2d $(EXEDIR)/spde2d
verycleanlib:
(cd ../..; make veryclean)

458
tests/pdegen/ppde2d.f90
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@ -0,0 +1,458 @@
!!$
!!$
!!$ MLD2P4 version 2.0
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0)
!!$
!!$ (C) Copyright 2008,2009,2010,2012
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$
!!$ 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 MLD2P4 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 MLD2P4 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: ppde2d.f90
!
! Program: ppde2d
! 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.
!
program ppde2d
use psb_base_mod
use mld_prec_mod
use psb_krylov_mod
use psb_util_mod
use data_input
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
! sparse matrix and preconditioner
type(psb_dspmat_type) :: a
type(mld_dprec_type) :: prec
! descriptor
type(psb_desc_type) :: desc_a
! dense vectors
type(psb_d_vect_type) :: x,b
! parallel environment
integer(psb_ipk_) :: ictxt, iam, np
! solver parameters
integer :: iter, itmax,itrace, istopc, irst, nlv
integer(psb_long_int_k_) :: amatsize, precsize, descsize
real(psb_dpk_) :: err, eps
type precdata
character(len=20) :: descr ! verbose description of the prec
character(len=10) :: prec ! overall prectype
integer :: novr ! number of overlap layers
integer :: jsweeps ! Jacobi/smoother sweeps
character(len=16) :: restr ! restriction over application of as
character(len=16) :: prol ! prolongation over application of as
character(len=16) :: solve ! Solver type: ILU, SuperLU, UMFPACK.
integer :: fill1 ! Fill-in for factorization 1
real(psb_dpk_) :: thr1 ! Threshold for fact. 1 ILU(T)
character(len=16) :: smther ! Smoother
integer :: nlev ! Number of levels in multilevel prec.
character(len=16) :: aggrkind ! smoothed/raw aggregatin
character(len=16) :: aggr_alg ! local or global aggregation
character(len=16) :: mltype ! additive or multiplicative 2nd level prec
character(len=16) :: smthpos ! side: pre, post, both smoothing
character(len=16) :: cmat ! coarse mat
character(len=16) :: csolve ! Coarse solver: bjac, umf, slu, sludist
character(len=16) :: csbsolve ! Coarse subsolver: ILU, ILU(T), SuperLU, UMFPACK.
integer :: cfill ! Fill-in for factorization 1
real(psb_dpk_) :: cthres ! Threshold for fact. 1 ILU(T)
integer :: cjswp ! Jacobi sweeps
real(psb_dpk_) :: athres ! smoother aggregation threshold
end type precdata
type(precdata) :: prectype
type(psb_d_coo_sparse_mat) :: acoo
! other variables
integer :: info, i
character(len=20) :: name,ch_err
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(2)
!
! Hello world
!
if (iam == psb_root_) then
write(*,*) 'Welcome to MLD2P4 version: ',mld_version_string_
write(*,*) 'This is the ',trim(name),' sample program'
end if
!
! get parameters
!
call get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
!
! 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,b,x,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 (psb_toupper(prectype%prec) == 'ML') then
nlv = prectype%nlev
call mld_precinit(prec,prectype%prec, info, nlev=nlv)
call mld_precset(prec,mld_smoother_type_, prectype%smther, info)
call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
call mld_precset(prec,mld_aggr_kind_, prectype%aggrkind,info)
call mld_precset(prec,mld_aggr_alg_, prectype%aggr_alg,info)
call mld_precset(prec,mld_ml_type_, prectype%mltype, info)
call mld_precset(prec,mld_smoother_pos_, prectype%smthpos, info)
if (prectype%athres >= dzero) &
& call mld_precset(prec,mld_aggr_thresh_, prectype%athres, info)
call mld_precset(prec,mld_coarse_solve_, prectype%csolve, info)
call mld_precset(prec,mld_coarse_subsolve_, prectype%csbsolve,info)
call mld_precset(prec,mld_coarse_mat_, prectype%cmat, info)
call mld_precset(prec,mld_coarse_fillin_, prectype%cfill, info)
call mld_precset(prec,mld_coarse_iluthrs_, prectype%cthres, info)
call mld_precset(prec,mld_coarse_sweeps_, prectype%cjswp, info)
else
nlv = 1
call mld_precinit(prec,prectype%prec, info, nlev=nlv)
call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
end if
call psb_barrier(ictxt)
t1 = psb_wtime()
call mld_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 prec%dump(info,prefix='test-ml',ac=.true.,solver=.true.,smoother=.true.)
call psb_amx(ictxt,tprec)
if (iam == psb_root_) &
& write(psb_out_unit,'("Preconditioner time : ",es12.5)')tprec
if (iam == psb_root_) call mld_precdescr(prec,info)
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()
call psb_krylov(kmethd,a,prec,b,x,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 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 DESC_A: ",i12)') descsize
write(psb_out_unit,'("Total memory occupation for PREC: ",i12)') precsize
end if
!
! cleanup storage and exit
!
call psb_gefree(b,desc_a,info)
call psb_gefree(x,desc_a,info)
call psb_spfree(a,desc_a,info)
call mld_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,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
integer :: ictxt
type(precdata) :: prectype
character(len=*) :: kmethd, afmt
integer :: idim, istopc,itmax,itrace,irst
integer :: np, iam, info
real(psb_dpk_) :: eps
character(len=20) :: buffer
call psb_info(ictxt, iam, np)
if (iam == psb_root_) then
call read_data(kmethd,5)
call read_data(afmt,5)
call read_data(idim,5)
call read_data(istopc,5)
call read_data(itmax,5)
call read_data(itrace,5)
call read_data(irst,5)
call read_data(eps,5)
call read_data(prectype%descr,5) ! verbose description of the prec
call read_data(prectype%prec,5) ! overall prectype
call read_data(prectype%novr,5) ! number of overlap layers
call read_data(prectype%restr,5) ! restriction over application of as
call read_data(prectype%prol,5) ! prolongation over application of as
call read_data(prectype%solve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%fill1,5) ! Fill-in for factorization 1
call read_data(prectype%thr1,5) ! Threshold for fact. 1 ILU(T)
call read_data(prectype%jsweeps,5) ! Jacobi sweeps for PJAC
if (psb_toupper(prectype%prec) == 'ML') then
call read_data(prectype%smther,5) ! Smoother type.
call read_data(prectype%nlev,5) ! Number of levels in multilevel prec.
call read_data(prectype%aggrkind,5) ! smoothed/raw aggregatin
call read_data(prectype%aggr_alg,5) ! local or global aggregation
call read_data(prectype%mltype,5) ! additive or multiplicative 2nd level prec
call read_data(prectype%smthpos,5) ! side: pre, post, both smoothing
call read_data(prectype%cmat,5) ! coarse mat
call read_data(prectype%csolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%csbsolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%cfill,5) ! Fill-in for factorization 1
call read_data(prectype%cthres,5) ! Threshold for fact. 1 ILU(T)
call read_data(prectype%cjswp,5) ! Jacobi sweeps
call read_data(prectype%athres,5) ! smoother aggr thresh
end if
end if
! broadcast parameters to all processors
call psb_bcast(ictxt,kmethd)
call psb_bcast(ictxt,afmt)
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)
call psb_bcast(ictxt,eps)
call psb_bcast(ictxt,prectype%descr) ! verbose description of the prec
call psb_bcast(ictxt,prectype%prec) ! overall prectype
call psb_bcast(ictxt,prectype%novr) ! number of overlap layers
call psb_bcast(ictxt,prectype%restr) ! restriction over application of as
call psb_bcast(ictxt,prectype%prol) ! prolongation over application of as
call psb_bcast(ictxt,prectype%solve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%fill1) ! Fill-in for factorization 1
call psb_bcast(ictxt,prectype%thr1) ! Threshold for fact. 1 ILU(T)
call psb_bcast(ictxt,prectype%jsweeps) ! Jacobi sweeps
if (psb_toupper(prectype%prec) == 'ML') then
call psb_bcast(ictxt,prectype%smther) ! Smoother type.
call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec.
call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin
call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation
call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec
call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing
call psb_bcast(ictxt,prectype%cmat) ! coarse mat
call psb_bcast(ictxt,prectype%csolve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%csbsolve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%cfill) ! Fill-in for factorization 1
call psb_bcast(ictxt,prectype%cthres) ! Threshold for fact. 1 ILU(T)
call psb_bcast(ictxt,prectype%cjswp) ! Jacobi sweeps
call psb_bcast(ictxt,prectype%athres) ! smoother aggr thresh
end if
if (iam == psb_root_) then
write(psb_out_unit,'("Solving 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,'("Preconditioner : ",a)') prectype%descr
write(psb_out_unit,'("Iterative method : ",a)') kmethd
write(psb_out_unit,'(" ")')
endif
return
end subroutine get_parms
!
! print an error message
!
subroutine pr_usage(iout)
integer :: 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
!
! functions parametrizing the differential equation
!
function b1(x,y)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_), intent(in) :: x,y
b1=1.d0/sqrt(2.d0)
end function b1
function b2(x,y)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_), intent(in) :: x,y
b2=1.d0/sqrt(2.d0)
end function b2
function c(x,y)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: c
real(psb_dpk_), intent(in) :: x,y
c=0.d0
end function c
function a1(x,y)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_), intent(in) :: x,y
a1=1.d0/80
end function a1
function a2(x,y)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_), intent(in) :: x,y
a2=1.d0/80
end function a2
function g(x,y)
use psb_base_mod, only : psb_dpk_, done
real(psb_dpk_) :: g
real(psb_dpk_), intent(in) :: x,y
g = dzero
if (x == done) then
g = done
else if (x == dzero) then
g = exp(-y**2)
end if
end function g
end program ppde2d

422
tests/pdegen/ppde.f90 → tests/pdegen/ppde3d.f90
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@ -4,7 +4,7 @@
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0)
!!$
!!$ (C) Copyright 2008,2009,2010
!!$ (C) Copyright 2008,2009,2010,2012
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
@ -36,39 +36,34 @@
!!$ POSSIBILITY OF SUCH DAMAGE.
!!$
!!$
! File: ppde.f90
!
! Program: ppde
! File: ppde3d.f90
!
! Program: ppde3d
! 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
! 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
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
! on the unit cube 0<=x,y,z<=1.
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
!
! Note that if b1=b2=b3=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.
!
! 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 ppde
program ppde3d
use psb_base_mod
use mld_prec_mod
use psb_krylov_mod
@ -91,8 +86,7 @@ program ppde
! descriptor
type(psb_desc_type) :: desc_a
! dense matrices
type(psb_d_vect_type) :: x,b, vtst
real(psb_dpk_), allocatable :: tst(:)
type(psb_d_vect_type) :: x,b
! blacs parameters
integer :: ictxt, iam, np
@ -164,7 +158,8 @@ program ppde
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,afmt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@ -419,333 +414,60 @@ contains
end subroutine pr_usage
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs.
!
subroutine create_matrix(idim,a,b,xv,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
implicit none
integer :: idim
integer, parameter :: nb=20
type(psb_d_vect_type) :: b,xv
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_dspmat_type) :: a
real(psb_dpk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner
integer :: np, iam, nr, nt
integer :: element
integer, 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=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 :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
sqdeltah = deltah*deltah
deltah2 = 2.d0* 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(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,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)/sqdeltah-a1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/sqdeltah-a1(x,y,z)/deltah2
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)/sqdeltah-a2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/sqdeltah-a2(x,y,z)/deltah2
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)/sqdeltah-a3(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/sqdeltah-a3(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,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/sqdeltah&
& +a4(x,y,z)
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)=-b3(x,y,z)/sqdeltah+a3(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/sqdeltah+a3(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)/sqdeltah+a2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/sqdeltah+a2(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)=-b1(x,y,z)/sqdeltah+a1(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/sqdeltah+a1(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),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
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(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
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,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
ch_err = a%get_fmt()
write(psb_out_unit,&
& '("The matrix has been generated and assembled in ",a3," format.")')&
& ch_err(1:3)
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
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b1
real(psb_dpk_), intent(in) :: x,y,z
b1=1.d0/sqrt(3.d0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b2
real(psb_dpk_), intent(in) :: x,y,z
b2=1.d0/sqrt(3.d0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: b3
real(psb_dpk_), intent(in) :: x,y,z
b3=1.d0/sqrt(3.d0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: c
real(psb_dpk_), intent(in) :: x,y,z
c=0.d0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a1
real(psb_dpk_), intent(in) :: x,y,z
a1=1.d0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a2
real(psb_dpk_), intent(in) :: x,y,z
a2=1.d0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_dpk_
real(psb_dpk_) :: a3
real(psb_dpk_), intent(in) :: x,y,z
a3=1.d0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_dpk_, done
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
return
end subroutine create_matrix
end program ppde
!
! 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
end function g
end program ppde3d

457
tests/pdegen/spde2d.f90
Unescape Escape View File

@ -0,0 +1,457 @@
!!$
!!$
!!$ MLD2P4 version 2.0
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0)
!!$
!!$ (C) Copyright 2008,2009,2010,2012
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$
!!$ 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 MLD2P4 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 MLD2P4 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: 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.
!
program spde2d
use psb_base_mod
use mld_prec_mod
use psb_krylov_mod
use psb_util_mod
use data_input
implicit none
! input parameters
character(len=20) :: kmethd, ptype
character(len=5) :: afmt
integer :: idim
! miscellaneous
real(psb_spk_), parameter :: one = 1.0
real(psb_dpk_) :: t1, t2, tprec
! sparse matrix and preconditioner
type(psb_sspmat_type) :: a
type(mld_sprec_type) :: prec
! descriptor
type(psb_desc_type) :: desc_a
! dense matrices
type(psb_s_vect_type) :: x,b
! blacs parameters
integer :: ictxt, iam, np
! solver parameters
integer :: iter, itmax,itrace, istopc, irst, nlv
integer(psb_long_int_k_) :: amatsize, precsize, descsize
real(psb_spk_) :: err, eps
type precdata
character(len=20) :: descr ! verbose description of the prec
character(len=10) :: prec ! overall prectype
integer :: novr ! number of overlap layers
integer :: jsweeps ! Jacobi/smoother sweeps
character(len=16) :: restr ! restriction over application of as
character(len=16) :: prol ! prolongation over application of as
character(len=16) :: solve ! Solver type: ILU, SuperLU, UMFPACK.
integer :: fill1 ! Fill-in for factorization 1
real(psb_spk_) :: thr1 ! Threshold for fact. 1 ILU(T)
character(len=16) :: smther ! Smoother
integer :: nlev ! Number of levels in multilevel prec.
character(len=16) :: aggrkind ! smoothed/raw aggregatin
character(len=16) :: aggr_alg ! local or global aggregation
character(len=16) :: mltype ! additive or multiplicative 2nd level prec
character(len=16) :: smthpos ! side: pre, post, both smoothing
character(len=16) :: cmat ! coarse mat
character(len=16) :: csolve ! Coarse solver: bjac, umf, slu, sludist
character(len=16) :: csbsolve ! Coarse subsolver: ILU, ILU(T), SuperLU, UMFPACK.
integer :: cfill ! Fill-in for factorization 1
real(psb_spk_) :: cthres ! Threshold for fact. 1 ILU(T)
integer :: cjswp ! Jacobi sweeps
real(psb_spk_) :: athres ! smoother aggregation threshold
end type precdata
type(precdata) :: prectype
type(psb_s_coo_sparse_mat) :: acoo
! other variables
integer :: info
character(len=20) :: name,ch_err
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(2)
!
! Hello world
!
if (iam == psb_root_) then
write(*,*) 'Welcome to MLD2P4 version: ',mld_version_string_
write(*,*) 'This is the ',trim(name),' sample program'
end if
!
! get parameters
!
call get_parms(ictxt,kmethd,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
!
! 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,b,x,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 (psb_toupper(prectype%prec) == 'ML') then
nlv = prectype%nlev
call mld_precinit(prec,prectype%prec, info, nlev=nlv)
call mld_precset(prec,mld_smoother_type_, prectype%smther, info)
call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
call mld_precset(prec,mld_aggr_kind_, prectype%aggrkind,info)
call mld_precset(prec,mld_aggr_alg_, prectype%aggr_alg,info)
call mld_precset(prec,mld_ml_type_, prectype%mltype, info)
call mld_precset(prec,mld_smoother_pos_, prectype%smthpos, info)
if (prectype%athres >= szero) &
& call mld_precset(prec,mld_aggr_thresh_, prectype%athres, info)
call mld_precset(prec,mld_coarse_solve_, prectype%csolve, info)
call mld_precset(prec,mld_coarse_subsolve_, prectype%csbsolve,info)
call mld_precset(prec,mld_coarse_mat_, prectype%cmat, info)
call mld_precset(prec,mld_coarse_fillin_, prectype%cfill, info)
call mld_precset(prec,mld_coarse_iluthrs_, prectype%cthres, info)
call mld_precset(prec,mld_coarse_sweeps_, prectype%cjswp, info)
else
nlv = 1
call mld_precinit(prec,prectype%prec, info, nlev=nlv)
call mld_precset(prec,mld_smoother_sweeps_, prectype%jsweeps, info)
call mld_precset(prec,mld_sub_ovr_, prectype%novr, info)
call mld_precset(prec,mld_sub_restr_, prectype%restr, info)
call mld_precset(prec,mld_sub_prol_, prectype%prol, info)
call mld_precset(prec,mld_sub_solve_, prectype%solve, info)
call mld_precset(prec,mld_sub_fillin_, prectype%fill1, info)
call mld_precset(prec,mld_sub_iluthrs_, prectype%thr1, info)
end if
call psb_barrier(ictxt)
t1 = psb_wtime()
call mld_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 prec%dump(info,prefix='test-ml',ac=.true.,solver=.true.,smoother=.true.)
call psb_amx(ictxt,tprec)
if (iam == psb_root_) &
& write(psb_out_unit,'("Preconditioner time : ",es12.5)')tprec
if (iam == psb_root_) call mld_precdescr(prec,info)
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()
call psb_krylov(kmethd,a,prec,b,x,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 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 DESC_A: ",i12)') descsize
write(psb_out_unit,'("Total memory occupation for PREC: ",i12)') precsize
end if
!
! cleanup storage and exit
!
call psb_gefree(b,desc_a,info)
call psb_gefree(x,desc_a,info)
call psb_spfree(a,desc_a,info)
call mld_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,prectype,afmt,idim,istopc,itmax,itrace,irst,eps)
integer :: ictxt
type(precdata) :: prectype
character(len=*) :: kmethd, afmt
integer :: idim, istopc,itmax,itrace,irst
integer :: np, iam, info
real(psb_spk_) :: eps
character(len=20) :: buffer
call psb_info(ictxt, iam, np)
if (iam == psb_root_) then
call read_data(kmethd,5)
call read_data(afmt,5)
call read_data(idim,5)
call read_data(istopc,5)
call read_data(itmax,5)
call read_data(itrace,5)
call read_data(irst,5)
call read_data(eps,5)
call read_data(prectype%descr,5) ! verbose description of the prec
call read_data(prectype%prec,5) ! overall prectype
call read_data(prectype%novr,5) ! number of overlap layers
call read_data(prectype%restr,5) ! restriction over application of as
call read_data(prectype%prol,5) ! prolongation over application of as
call read_data(prectype%solve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%fill1,5) ! Fill-in for factorization 1
call read_data(prectype%thr1,5) ! Threshold for fact. 1 ILU(T)
call read_data(prectype%jsweeps,5) ! Jacobi sweeps for PJAC
if (psb_toupper(prectype%prec) == 'ML') then
call read_data(prectype%smther,5) ! Smoother type.
call read_data(prectype%nlev,5) ! Number of levels in multilevel prec.
call read_data(prectype%aggrkind,5) ! smoothed/raw aggregatin
call read_data(prectype%aggr_alg,5) ! local or global aggregation
call read_data(prectype%mltype,5) ! additive or multiplicative 2nd level prec
call read_data(prectype%smthpos,5) ! side: pre, post, both smoothing
call read_data(prectype%cmat,5) ! coarse mat
call read_data(prectype%csolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%csbsolve,5) ! Factorization type: ILU, SuperLU, UMFPACK.
call read_data(prectype%cfill,5) ! Fill-in for factorization 1
call read_data(prectype%cthres,5) ! Threshold for fact. 1 ILU(T)
call read_data(prectype%cjswp,5) ! Jacobi sweeps
call read_data(prectype%athres,5) ! smoother aggr thresh
end if
end if
! broadcast parameters to all processors
call psb_bcast(ictxt,kmethd)
call psb_bcast(ictxt,afmt)
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)
call psb_bcast(ictxt,eps)
call psb_bcast(ictxt,prectype%descr) ! verbose description of the prec
call psb_bcast(ictxt,prectype%prec) ! overall prectype
call psb_bcast(ictxt,prectype%novr) ! number of overlap layers
call psb_bcast(ictxt,prectype%restr) ! restriction over application of as
call psb_bcast(ictxt,prectype%prol) ! prolongation over application of as
call psb_bcast(ictxt,prectype%solve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%fill1) ! Fill-in for factorization 1
call psb_bcast(ictxt,prectype%thr1) ! Threshold for fact. 1 ILU(T)
call psb_bcast(ictxt,prectype%jsweeps) ! Jacobi sweeps
if (psb_toupper(prectype%prec) == 'ML') then
call psb_bcast(ictxt,prectype%smther) ! Smoother type.
call psb_bcast(ictxt,prectype%nlev) ! Number of levels in multilevel prec.
call psb_bcast(ictxt,prectype%aggrkind) ! smoothed/raw aggregatin
call psb_bcast(ictxt,prectype%aggr_alg) ! local or global aggregation
call psb_bcast(ictxt,prectype%mltype) ! additive or multiplicative 2nd level prec
call psb_bcast(ictxt,prectype%smthpos) ! side: pre, post, both smoothing
call psb_bcast(ictxt,prectype%cmat) ! coarse mat
call psb_bcast(ictxt,prectype%csolve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%csbsolve) ! Factorization type: ILU, SuperLU, UMFPACK.
call psb_bcast(ictxt,prectype%cfill) ! Fill-in for factorization 1
call psb_bcast(ictxt,prectype%cthres) ! Threshold for fact. 1 ILU(T)
call psb_bcast(ictxt,prectype%cjswp) ! Jacobi sweeps
call psb_bcast(ictxt,prectype%athres) ! smoother aggr thresh
end if
if (iam == psb_root_) then
write(psb_out_unit,'("Solving 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,'("Preconditioner : ",a)') prectype%descr
write(psb_out_unit,'("Iterative method : ",a)') kmethd
write(psb_out_unit,'(" ")')
endif
return
end subroutine get_parms
!
! print an error message
!
subroutine pr_usage(iout)
integer :: 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
!
! 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
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 program spde2d

423
tests/pdegen/spde.f90 → tests/pdegen/spde3d.f90
Unescape Escape View File

@ -4,7 +4,7 @@
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 3.0)
!!$
!!$ (C) Copyright 2008,2009,2010
!!$ (C) Copyright 2008,2009,2010,2012
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
@ -36,39 +36,34 @@
!!$ POSSIBILITY OF SUCH DAMAGE.
!!$
!!$
! File: ppde.f90
!
! Program: ppde
! File: spde3d.f90
!
! Program: spde3d
! 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
! 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
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
! on the unit cube 0<=x,y,z<=1.
!
! Example taken from:
! C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
!
! Note that if b1=b2=b3=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.
!
! 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 spde
program spde3d
use psb_base_mod
use mld_prec_mod
use psb_krylov_mod
@ -91,8 +86,7 @@ program spde
! descriptor
type(psb_desc_type) :: desc_a
! dense matrices
type(psb_s_vect_type) :: x,b, vtst
real(psb_spk_), allocatable :: tst(:)
type(psb_s_vect_type) :: x,b
! blacs parameters
integer :: ictxt, iam, np
@ -164,7 +158,8 @@ program spde
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,ictxt,afmt,info)
call psb_gen_pde3d(ictxt,idim,a,b,x,desc_a,afmt,&
& a1,a2,a3,b1,b2,b3,c,g,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
@ -417,335 +412,61 @@ contains
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,b,xv,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
implicit none
integer :: idim
integer, parameter :: nb=20
type(psb_s_vect_type) :: b,xv
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
type(psb_sspmat_type) :: a
real(psb_spk_) :: zt(nb),x,y,z
integer :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer :: ix,iy,iz,ia,indx_owner
integer :: np, iam, nr, nt
integer :: element
integer, 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=0.0,one=1.0,zero=0.0
real(psb_dpk_) :: t0, t1, t2, t3, tasb, talc, ttot, tgen
real(psb_spk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
character(len=20) :: name, ch_err
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.0/(idim-1)
sqdeltah = deltah*deltah
deltah2 = 2.0* 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(b,desc_a,info)
if (info == psb_success_) call psb_geall(xv,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)/sqdeltah-a1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/sqdeltah-a1(x,y,z)/deltah2
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)/sqdeltah-a2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/sqdeltah-a2(x,y,z)/deltah2
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)/sqdeltah-a3(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/sqdeltah-a3(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,z)
val(element)=(2*b1(x,y,z) + 2*b2(x,y,z) + 2*b3(x,y,z))/sqdeltah&
& +a4(x,y,z)
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)=-b3(x,y,z)/sqdeltah+a3(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/sqdeltah+a3(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)/sqdeltah+a2(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(x,y,z)/sqdeltah+a2(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)=-b1(x,y,z)/sqdeltah+a1(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(x,y,z)/sqdeltah+a1(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),b,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
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(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
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,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
ch_err = a%get_fmt()
write(psb_out_unit,&
& '("The matrix has been generated and assembled in ",a3," format.")')&
& ch_err(1:3)
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
! functions parametrizing the differential equation
!
function b1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b1
real(psb_spk_), intent(in) :: x,y,z
b1=1.e0/sqrt(3.e0)
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b2
real(psb_spk_), intent(in) :: x,y,z
b2=1.e0/sqrt(3.e0)
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b3
real(psb_spk_), intent(in) :: x,y,z
b3=1.e0/sqrt(3.e0)
end function b3
function c(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: c
real(psb_spk_), intent(in) :: x,y,z
c=0.e0
end function c
function a1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a1
real(psb_spk_), intent(in) :: x,y,z
a1=1.e0/80
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a2
real(psb_spk_), intent(in) :: x,y,z
a2=1.e0/80
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a3
real(psb_spk_), intent(in) :: x,y,z
a3=1.e0/80
end function a3
function g(x,y,z)
use psb_base_mod, only : psb_spk_, sone
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
return
end subroutine create_matrix
end program spde
!
! functions parametrizing the differential equation
!
function a1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a1
real(psb_spk_) :: x,y,z
a1=1.e0
end function a1
function a2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a2
real(psb_spk_) :: x,y,z
a2=2.e1*y
end function a2
function a3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a3
real(psb_spk_) :: x,y,z
a3=1.e0
end function a3
function a4(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: a4
real(psb_spk_) :: x,y,z
a4=1.e0
end function a4
function b1(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b1
real(psb_spk_) :: x,y,z
b1=1.e0
end function b1
function b2(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b2
real(psb_spk_) :: x,y,z
b2=1.e0
end function b2
function b3(x,y,z)
use psb_base_mod, only : psb_spk_
real(psb_spk_) :: b3
real(psb_spk_) :: x,y,z
b3=1.e0
end function b3
end function g
end program spde3d
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