!!$
!!$ Parallel Sparse BLAS version 2.2
!!$ (C) Copyright 2006/2007/2008
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari University of Rome Tor Vergata
!!$
!!$ 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 PSBLAS 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 PSBLAS 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: ppde.f90
!
! Program: ppde
! This sample program shows how to build and solve a sparse linear
!
! The program solves a linear system based on the partial differential
! equation
!
!
!
! The equation generated is
!
! b1 d d (u) b2 d d (u) a1 d (u)) a2 d (u)))
! - ------ - ------ + ----- + ------ + a3 u = 0
! dx dx dy dy dx dy
!
!
! with Dirichlet boundary conditions on the unit cube
!
! 0<=x,y,z<=1
!
! The equation is discretized with finite differences and uniform stepsize;
! the resulting discrete equation is
!
! ( u(x,y,z)(2b1+2b2+a1+a2)+u(x-1,y)(-b1-a1)+u(x,y-1)(-b2-a2)+
! -u(x+1,y)b1-u(x,y+1)b2)*(1/h**2)
!
! Example taken from: C.T.Kelley
! Iterative Methods for Linear and Nonlinear Equations
! SIAM 1995
!
!
! 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) = rhs(x,y)
!
program ppde
use psb_base_mod
use psb_prec_mod
use psb_krylov_mod
use psb_util_mod
implicit none
! input parameters
character(len=20) :: kmethd, ptype
character(len=5) :: afmt
integer :: 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(psb_dprec_type) :: prec
! descriptor
type(psb_desc_type) :: desc_a
! dense matrices
real(psb_dpk_), allocatable :: b(:), x(:)
! blacs parameters
integer :: ictxt, iam, np
! solver parameters
integer :: iter, itmax,itrace, istopc, irst
real(psb_dpk_) :: err, eps
! other variables
integer :: info
character(len=20) :: name,ch_err
info=0
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='pde90'
call psb_set_errverbosity(2)
!
! get parameters
!
call get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst)
!
! allocate and fill in the coefficient matrix, rhs and initial guess
!
call psb_cd_set_large_threshold(128)
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,b,x,desc_a,part_block,ictxt,afmt,info)
t2 = psb_wtime() - t1
if(info /= 0) then
info=4010
ch_err='create_matrix'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
call psb_amx(ictxt,t2)
if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es10.4)')t2
if (iam == psb_root_) write(*,'(" ")')
!
! prepare the preconditioner.
!
if(iam == psb_root_) write(0,'("Setting preconditioner to : ",a)')ptype
call psb_precinit(prec,ptype,info)
call psb_barrier(ictxt)
t1 = psb_wtime()
call psb_precbld(a,desc_a,prec,info)
if(info /= 0) then
info=4010
ch_err='psb_precbld'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
tprec = psb_wtime()-t1
call psb_amx(ictxt,tprec)
if (iam == psb_root_) write(*,'("Preconditioner time : ",es10.4)')tprec
if (iam == psb_root_) write(*,'(" ")')
!
! iterative method parameters
!
if(iam == psb_root_) write(*,'("Calling iterative method ",a)')kmethd
call psb_barrier(ictxt)
t1 = psb_wtime()
eps = 1.d-9
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 /= 0) then
info=4010
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)
if (iam == psb_root_) then
write(*,'(" ")')
write(*,'("Time to solve matrix : ",es10.4)')t2
write(*,'("Time per iteration : ",es10.4)')t2/iter
write(*,'("Number of iterations : ",i0)')iter
write(*,'("Error estimate on exit : ",es10.4)')err
write(*,'("Info on exit : ",i0)')info
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 psb_precfree(prec,info)
call psb_cdfree(desc_a,info)
if(info /= 0) then
info=4010
ch_err='free routine'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
9999 continue
if(info /= 0) then
call psb_error(ictxt)
end if
call psb_exit(ictxt)
stop
contains
!
! get iteration parameters from the command line
!
subroutine get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst)
integer :: ictxt
character(len=*) :: kmethd, ptype, afmt
integer :: idim, istopc,itmax,itrace,irst
integer :: np, iam
integer :: intbuf(10), ip
call psb_info(ictxt, iam, np)
if (iam==0) then
read(*,*) ip
if (ip >= 3) then
read(*,*) kmethd
read(*,*) ptype
read(*,*) afmt
! broadcast parameters to all processors
call psb_bcast(ictxt,kmethd)
call psb_bcast(ictxt,afmt)
call psb_bcast(ictxt,ptype)
read(*,*) idim
if (ip >= 4) then
read(*,*) istopc
else
istopc=1
endif
if (ip >= 5) then
read(*,*) itmax
else
itmax=500
endif
if (ip >= 6) then
read(*,*) itrace
else
itrace=-1
endif
if (ip >= 7) then
read(*,*) irst
else
irst=1
endif
! broadcast parameters to all processors
intbuf(1) = idim
intbuf(2) = istopc
intbuf(3) = itmax
intbuf(4) = itrace
intbuf(5) = irst
call psb_bcast(ictxt,intbuf(1:5))
write(*,'("Solving matrix : ell1")')
write(*,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim
write(*,'("Number of processors : ",i0)')np
write(*,'("Data distribution : BLOCK")')
write(*,'("Preconditioner : ",a)') ptype
write(*,'("Iterative method : ",a)') kmethd
write(*,'(" ")')
else
! wrong number of parameter, print an error message and exit
call pr_usage(0)
call psb_abort(ictxt)
stop 1
endif
else
call psb_bcast(ictxt,kmethd)
call psb_bcast(ictxt,afmt)
call psb_bcast(ictxt,ptype)
call psb_bcast(ictxt,intbuf(1:5))
idim = intbuf(1)
istopc = intbuf(2)
itmax = intbuf(3)
itrace = intbuf(4)
irst = intbuf(5)
end if
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
!
! subroutine to allocate and fill in the coefficient matrix and
! the rhs.
!
subroutine create_matrix(idim,a,b,xv,desc_a,parts,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
!
! = 0
!
! boundary condition: dirichlet
! 0< x,y,z<1
!
! u(x,y,z)(2b1+2b2+2b3+a1+a2+a3)+u(x-1,y,z)(-b1-a1)+u(x,y-1,z)(-b2-a2)+
! + u(x,y,z-1)(-b3-a3)-u(x+1,y,z)b1-u(x,y+1,z)b2-u(x,y,z+1)b3
use psb_base_mod
implicit none
integer :: idim
integer, parameter :: nbmax=10
real(psb_dpk_), allocatable :: b(:),xv(:)
type(psb_desc_type) :: desc_a
integer :: ictxt, info
character :: afmt*5
interface
! .....user passed subroutine.....
subroutine parts(global_indx,n,np,pv,nv)
implicit none
integer, intent(in) :: global_indx, n, np
integer, intent(out) :: nv
integer, intent(out) :: pv(*)
end subroutine parts
end interface ! local variables
type(psb_dspmat_type) :: a
real(psb_dpk_) :: zt(nbmax),glob_x,glob_y,glob_z
integer :: m,n,nnz,glob_row
integer :: x,y,z,ia,indx_owner
integer :: np, iam
integer :: element
integer :: nv, inv
integer, allocatable :: irow(:),icol(:)
real(psb_dpk_), allocatable :: val(:)
integer, allocatable :: prv(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_dpk_) :: deltah
real(psb_dpk_),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
real(psb_dpk_) :: t1, t2, t3, tins, tasb
real(psb_dpk_) :: a1, a2, a3, a4, b1, b2, b3
external :: a1, a2, a3, a4, b1, b2, b3
integer :: err_act
! common area
character(len=20) :: name, ch_err
info = 0
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
! 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(0,'("Generating Matrix (size=",i0x,")...")')n
call psb_cdall(ictxt,desc_a,info,mg=n,parts=parts)
call psb_spall(a,desc_a,info,nnz=nnz)
! define rhs from boundary conditions; also build initial guess
call psb_geall(b,desc_a,info)
call psb_geall(xv,desc_a,info)
if(info /= 0) then
info=4010
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*nbmax),irow(20*nbmax),&
&icol(20*nbmax),prv(np),stat=info)
if (info /= 0 ) then
info=4000
call psb_errpush(info,name)
goto 9999
endif
tins = 0.d0
call psb_barrier(ictxt)
t1 = psb_wtime()
! loop over rows belonging to current process in a block
! distribution.
! icol(1)=1
do glob_row = 1, n
call parts(glob_row,n,np,prv,nv)
do inv = 1, nv
indx_owner = prv(inv)
if (indx_owner == iam) then
! local matrix pointer
element=1
! compute gridpoint coordinates
if (mod(glob_row,(idim*idim)) == 0) then
x = glob_row/(idim*idim)
else
x = glob_row/(idim*idim)+1
endif
if (mod((glob_row-(x-1)*idim*idim),idim) == 0) then
y = (glob_row-(x-1)*idim*idim)/idim
else
y = (glob_row-(x-1)*idim*idim)/idim+1
endif
z = glob_row-(x-1)*idim*idim-(y-1)*idim
! glob_x, glob_y, glob_x coordinates
glob_x=x*deltah
glob_y=y*deltah
glob_z=z*deltah
! check on boundary points
zt(1) = 0.d0
! internal point: build discretization
!
! term depending on (x-1,y,z)
!
if (x==1) then
val(element)=-b1(glob_x,glob_y,glob_z)&
& -a1(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
zt(1) = exp(-glob_y**2-glob_z**2)*(-val(element))
else
val(element)=-b1(glob_x,glob_y,glob_z)&
& -a1(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-2)*idim*idim+(y-1)*idim+(z)
element=element+1
endif
! term depending on (x,y-1,z)
if (y==1) then
val(element)=-b2(glob_x,glob_y,glob_z)&
& -a2(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
else
val(element)=-b2(glob_x,glob_y,glob_z)&
& -a2(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-1)*idim*idim+(y-2)*idim+(z)
element=element+1
endif
! term depending on (x,y,z-1)
if (z==1) then
val(element)=-b3(glob_x,glob_y,glob_z)&
& -a3(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
else
val(element)=-b3(glob_x,glob_y,glob_z)&
& -a3(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-1)*idim*idim+(y-1)*idim+(z-1)
element=element+1
endif
! term depending on (x,y,z)
val(element)=2*b1(glob_x,glob_y,glob_z)&
& +2*b2(glob_x,glob_y,glob_z)&
& +2*b3(glob_x,glob_y,glob_z)&
& +a1(glob_x,glob_y,glob_z)&
& +a2(glob_x,glob_y,glob_z)&
& +a3(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-1)*idim*idim+(y-1)*idim+(z)
element=element+1
! term depending on (x,y,z+1)
if (z==idim) then
val(element)=-b1(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
else
val(element)=-b1(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-1)*idim*idim+(y-1)*idim+(z+1)
element=element+1
endif
! term depending on (x,y+1,z)
if (y==idim) then
val(element)=-b2(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element))
else
val(element)=-b2(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x-1)*idim*idim+(y)*idim+(z)
element=element+1
endif
! term depending on (x+1,y,z)
if (x<idim) then
val(element)=-b3(glob_x,glob_y,glob_z)
val(element) = val(element)/(deltah*&
& deltah)
icol(element)=(x)*idim*idim+(y-1)*idim+(z)
element=element+1
endif
irow(1:element-1)=glob_row
ia=glob_row
t3 = psb_wtime()
call psb_spins(element-1,irow,icol,val,a,desc_a,info)
if(info /= 0) exit
tins = tins + (psb_wtime()-t3)
call psb_geins(1,(/ia/),zt(1:1),b,desc_a,info)
if(info /= 0) exit
zt(1)=0.d0
call psb_geins(1,(/ia/),zt(1:1),xv,desc_a,info)
if(info /= 0) exit
end if
end do
end do
call psb_barrier(ictxt)
t2 = psb_wtime()-t1
if(info /= 0) then
info=4010
ch_err='insert rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
deallocate(val,irow,icol)
t1 = psb_wtime()
call psb_cdasb(desc_a,info)
call psb_spasb(a,desc_a,info,dupl=psb_dupl_err_,afmt=afmt)
call psb_barrier(ictxt)
tasb = psb_wtime()-t1
if(info /= 0) then
info=4010
ch_err='asb rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
call psb_amx(ictxt,t2)
call psb_amx(ictxt,tins)
call psb_amx(ictxt,tasb)
if(iam == psb_root_) then
write(*,'("The matrix has been generated and assembled in ",a3," format.")')&
& a%fida(1:3)
write(*,'("-pspins time : ",es10.4)')tins
write(*,'("-insert time : ",es10.4)')t2
write(*,'("-assembly time : ",es10.4)')tasb
end if
call psb_geasb(b,desc_a,info)
call psb_geasb(xv,desc_a,info)
if(info /= 0) then
info=4010
ch_err='asb rout.'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
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
end if
return
end subroutine create_matrix
end program ppde
!
! functions parametrizing the differential equation
!
function a1(x,y,z)
use psb_base_mod
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
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
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
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
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
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
real(psb_dpk_) :: b3
real(psb_dpk_) :: x,y,z
b3=1.d0
end function b3