|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! 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 an HPF BLOCK
|
|
|
|
|
! distribution directive.
|
|
|
|
|
!
|
|
|
|
|
! Boundary conditions are set in a very simple way, by adding
|
|
|
|
|
! equations of the form
|
|
|
|
|
!
|
|
|
|
|
! u(x,y) = rhs(x,y)
|
|
|
|
|
!
|
|
|
|
|
program pde90
|
|
|
|
|
use psb_sparse_mod
|
|
|
|
|
use psb_error_mod
|
|
|
|
|
implicit none
|
|
|
|
|
|
|
|
|
|
interface
|
|
|
|
|
!.....user passed subroutine.....
|
|
|
|
|
subroutine part_block(glob_index,n,np,pv,nv)
|
|
|
|
|
integer, intent(in) :: glob_index, n, np
|
|
|
|
|
integer, intent(out) :: nv
|
|
|
|
|
integer, intent(out) :: pv(*)
|
|
|
|
|
end subroutine part_block
|
|
|
|
|
end interface
|
|
|
|
|
! input parameters
|
|
|
|
|
character :: cmethd*10, prec*10, afmt*5
|
|
|
|
|
integer :: idim, iret
|
|
|
|
|
|
|
|
|
|
! miscellaneous
|
|
|
|
|
character, parameter :: order='r'
|
|
|
|
|
integer :: iargc,convert_descr,dim, check_descr
|
|
|
|
|
real(kind(1.d0)), parameter :: dzero = 0.d0, one = 1.d0
|
|
|
|
|
real(kind(1.d0)) :: mpi_wtime, t1, t2, tprec, tsolve, t3, t4
|
|
|
|
|
external mpi_wtime
|
|
|
|
|
|
|
|
|
|
! sparse matrix and preconditioner
|
|
|
|
|
type(psb_dspmat_type) :: a, l, u, h
|
|
|
|
|
type(psb_dprec_type) :: pre
|
|
|
|
|
! descriptor
|
|
|
|
|
type(psb_desc_type) :: desc_a, desc_a_out
|
|
|
|
|
! dense matrices
|
|
|
|
|
real(kind(1.d0)), pointer :: b(:), x(:), d(:),ld(:)
|
|
|
|
|
integer, pointer :: work(:)
|
|
|
|
|
! blacs parameters
|
|
|
|
|
integer :: nprow, npcol, icontxt, iam, np, myprow, mypcol
|
|
|
|
|
|
|
|
|
|
! solver parameters
|
|
|
|
|
integer :: iter, itmax,ierr,itrace, methd,iprec, istopc,&
|
|
|
|
|
& iparm(20), ml
|
|
|
|
|
real(kind(1.d0)) :: err, eps, rparm(20)
|
|
|
|
|
|
|
|
|
|
! other variables
|
|
|
|
|
integer :: i,info
|
|
|
|
|
integer :: internal, m,ii
|
|
|
|
|
character(len=10) :: ptype
|
|
|
|
|
character(len=20) :: name,ch_err
|
|
|
|
|
|
|
|
|
|
info=0
|
|
|
|
|
name='pde90'
|
|
|
|
|
call psb_set_errverbosity(2)
|
|
|
|
|
call psb_set_erraction(0)
|
|
|
|
|
|
|
|
|
|
! initialize blacs
|
|
|
|
|
call blacs_pinfo(iam, np)
|
|
|
|
|
call blacs_get(izero, izero, icontxt)
|
|
|
|
|
|
|
|
|
|
! rectangular grid, p x 1
|
|
|
|
|
|
|
|
|
|
call blacs_gridinit(icontxt, order, np, ione)
|
|
|
|
|
call blacs_gridinfo(icontxt, nprow, npcol, myprow, mypcol)
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! get parameters
|
|
|
|
|
!
|
|
|
|
|
call get_parms(icontxt,cmethd,prec,afmt,idim,istopc,itmax,itrace,ml)
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! allocate and fill in the coefficient matrix, rhs and initial guess
|
|
|
|
|
!
|
|
|
|
|
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t1 = mpi_wtime()
|
|
|
|
|
call create_matrix(idim,a,b,x,desc_a,part_block,icontxt,afmt,info)
|
|
|
|
|
t2 = mpi_wtime() - t1
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='create_matrix'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
dim=size(a%aspk)
|
|
|
|
|
|
|
|
|
|
!!$ allocate(h%aspk(dim),h%ia1(dim),h%ia2(dim),h%pl(size(a%pl)),&
|
|
|
|
|
!!$ & h%pl(size(a%pl)),d(size(a%pl)),&
|
|
|
|
|
!!$ & desc_a_out%matrix_data(size(desc_a%matrix_data)),&
|
|
|
|
|
!!$ & desc_a_out%halo_index(size(desc_a%halo_index)),&
|
|
|
|
|
!!$ & desc_a_out%ovrlap_index(size(desc_a%ovrlap_index)),&
|
|
|
|
|
!!$ & desc_a_out%ovrlap_elem(size(desc_a%ovrlap_elem)),&
|
|
|
|
|
!!$ & desc_a_out%loc_to_glob(size(desc_a%loc_to_glob)),&
|
|
|
|
|
!!$ & desc_a_out%glob_to_loc(size(desc_a%glob_to_loc)), work(1024))
|
|
|
|
|
!!$ check_descr=15
|
|
|
|
|
! work(5)=9
|
|
|
|
|
!!$ write(0,*)'calling verify'
|
|
|
|
|
!!$ call f90_psverify(d,a,desc_a,check_descr,convert_descr,h,&
|
|
|
|
|
!!$ & desc_a_out,work)
|
|
|
|
|
!!$ write(0,*)'verify done',convert_descr
|
|
|
|
|
|
|
|
|
|
! deallocate(work)
|
|
|
|
|
|
|
|
|
|
call dgamx2d(icontxt,'a',' ',ione, ione,t2,ione,t1,t1,-1,-1,-1)
|
|
|
|
|
if (iam.eq.0) write(6,*) 'matrix creation time : ',t2
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! prepare the preconditioner.
|
|
|
|
|
!
|
|
|
|
|
write(0,*)'precondizionatore=',prec
|
|
|
|
|
select case (prec)
|
|
|
|
|
case ('ILU')
|
|
|
|
|
iprec = 2
|
|
|
|
|
ptype='bja'
|
|
|
|
|
call psb_precset(pre,ptype)
|
|
|
|
|
case ('DIAGSC')
|
|
|
|
|
iprec = 1
|
|
|
|
|
ptype='diagsc'
|
|
|
|
|
call psb_precset(pre,ptype)
|
|
|
|
|
case ('NONE')
|
|
|
|
|
iprec = 0
|
|
|
|
|
ptype='noprec'
|
|
|
|
|
call psb_precset(pre,ptype)
|
|
|
|
|
case default
|
|
|
|
|
info=5003
|
|
|
|
|
ch_err(1:3)=prec(1:3)
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end select
|
|
|
|
|
write(0,*)'preconditioner set'
|
|
|
|
|
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t1 = mpi_wtime()
|
|
|
|
|
call psb_precbld(a,pre,desc_a,info)!,'f')
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='psb_precbld'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
tprec = mpi_wtime()-t1
|
|
|
|
|
|
|
|
|
|
call dgamx2d(icontxt,'a',' ',ione, ione,tprec,ione,t1,t1,-1,-1,-1)
|
|
|
|
|
|
|
|
|
|
if (iam.eq.0) write(6,*) 'preconditioner time : ',tprec
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! iterative method parameters
|
|
|
|
|
!
|
|
|
|
|
write(*,*) 'calling iterative method', a%ia2(7999:8001)
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t1 = mpi_wtime()
|
|
|
|
|
eps = 1.d-9
|
|
|
|
|
if (cmethd.eq.'BICGSTAB') then
|
|
|
|
|
call psb_bicgstab(a,pre,b,x,eps,desc_a,info,&
|
|
|
|
|
& itmax,iter,err,itrace)
|
|
|
|
|
else if (cmethd.eq.'CGS') then
|
|
|
|
|
call psb_cgs(a,pre,b,x,eps,desc_a,info,&
|
|
|
|
|
& itmax,iter,err,itrace)
|
|
|
|
|
else if (cmethd.eq.'BICGSTABL') then
|
|
|
|
|
call psb_bicgstabl(a,pre,b,x,eps,desc_a,info,&
|
|
|
|
|
& itmax,iter,err,itrace,ml)
|
|
|
|
|
else
|
|
|
|
|
write(0,*) 'unknown method ',cmethd
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='solver routine'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t2 = mpi_wtime() - t1
|
|
|
|
|
call dgamx2d(icontxt,'a',' ',ione, ione,t2,ione,t1,t1,-1,-1,-1)
|
|
|
|
|
|
|
|
|
|
if (iam.eq.0) then
|
|
|
|
|
write(6,*) 'time to solve matrix : ',t2
|
|
|
|
|
write(6,*) 'time per iteration : ',t2/iter
|
|
|
|
|
write(6,*) 'number of iterations : ',iter
|
|
|
|
|
write(6,*) 'error on exit : ',err
|
|
|
|
|
write(6,*) 'info on exit : ',ierr
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
!
|
|
|
|
|
! cleanup storage and exit
|
|
|
|
|
!
|
|
|
|
|
call psb_free(b,desc_a,info)
|
|
|
|
|
call psb_free(x,desc_a,info)
|
|
|
|
|
call psb_spfree(a,desc_a,info)
|
|
|
|
|
call psb_dscfree(desc_a,info)
|
|
|
|
|
if(info.ne.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(icontxt)
|
|
|
|
|
call blacs_gridexit(icontxt)
|
|
|
|
|
call blacs_exit(0)
|
|
|
|
|
else
|
|
|
|
|
call blacs_gridexit(icontxt)
|
|
|
|
|
call blacs_exit(0)
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
contains
|
|
|
|
|
!
|
|
|
|
|
! get iteration parameters from the command line
|
|
|
|
|
!
|
|
|
|
|
subroutine get_parms(icontxt,cmethd,prec,afmt,idim,istopc,itmax,itrace,ml)
|
|
|
|
|
integer :: icontxt
|
|
|
|
|
character :: cmethd*10, prec*10, afmt*5
|
|
|
|
|
integer :: idim, iret, istopc,itmax,itrace,ml
|
|
|
|
|
character*40 :: charbuf
|
|
|
|
|
integer :: iargc, nprow, npcol, myprow, mypcol
|
|
|
|
|
external iargc
|
|
|
|
|
integer :: intbuf(10), ip
|
|
|
|
|
|
|
|
|
|
call blacs_gridinfo(icontxt, nprow, npcol, myprow, mypcol)
|
|
|
|
|
|
|
|
|
|
if (myprow==0) then
|
|
|
|
|
read(*,*) ip
|
|
|
|
|
if (ip.ge.3) then
|
|
|
|
|
read(*,*) cmethd
|
|
|
|
|
read(*,*) prec
|
|
|
|
|
read(*,*) afmt
|
|
|
|
|
|
|
|
|
|
! convert strings in array
|
|
|
|
|
do i = 1, len(cmethd)
|
|
|
|
|
intbuf(i) = iachar(cmethd(i:i))
|
|
|
|
|
end do
|
|
|
|
|
! broadcast parameters to all processors
|
|
|
|
|
call igebs2d(icontxt,'ALL',' ',10,1,intbuf,10)
|
|
|
|
|
|
|
|
|
|
do i = 1, len(prec)
|
|
|
|
|
intbuf(i) = iachar(prec(i:i))
|
|
|
|
|
end do
|
|
|
|
|
! broadcast parameters to all processors
|
|
|
|
|
call igebs2d(icontxt,'ALL',' ',10,1,intbuf,10)
|
|
|
|
|
|
|
|
|
|
do i = 1, len(afmt)
|
|
|
|
|
intbuf(i) = iachar(afmt(i:i))
|
|
|
|
|
end do
|
|
|
|
|
! broadcast parameters to all processors
|
|
|
|
|
call igebs2d(icontxt,'ALL',' ',10,1,intbuf,10)
|
|
|
|
|
|
|
|
|
|
read(*,*) idim
|
|
|
|
|
if (ip.ge.4) then
|
|
|
|
|
read(*,*) istopc
|
|
|
|
|
else
|
|
|
|
|
istopc=1
|
|
|
|
|
endif
|
|
|
|
|
if (ip.ge.5) then
|
|
|
|
|
read(*,*) itmax
|
|
|
|
|
else
|
|
|
|
|
itmax=500
|
|
|
|
|
endif
|
|
|
|
|
if (ip.ge.6) then
|
|
|
|
|
read(*,*) itrace
|
|
|
|
|
else
|
|
|
|
|
itrace=-1
|
|
|
|
|
endif
|
|
|
|
|
if (ip.ge.7) then
|
|
|
|
|
read(*,*) ml
|
|
|
|
|
else
|
|
|
|
|
ml=1
|
|
|
|
|
endif
|
|
|
|
|
! broadcast parameters to all processors
|
|
|
|
|
|
|
|
|
|
intbuf(1) = idim
|
|
|
|
|
intbuf(2) = istopc
|
|
|
|
|
intbuf(3) = itmax
|
|
|
|
|
intbuf(4) = itrace
|
|
|
|
|
intbuf(5) = ml
|
|
|
|
|
call igebs2d(icontxt,'ALL',' ',5,1,intbuf,5)
|
|
|
|
|
|
|
|
|
|
write(6,*)'solving matrix: ell1'
|
|
|
|
|
write(6,*)'on grid',idim,'x',idim,'x',idim
|
|
|
|
|
write(6,*)' with block data distribution, np=',np,&
|
|
|
|
|
& ' preconditioner=',prec,&
|
|
|
|
|
& ' iterative methd=',cmethd
|
|
|
|
|
else
|
|
|
|
|
! wrong number of parameter, print an error message and exit
|
|
|
|
|
call pr_usage(0)
|
|
|
|
|
call blacs_abort(icontxt,-1)
|
|
|
|
|
stop 1
|
|
|
|
|
endif
|
|
|
|
|
else
|
|
|
|
|
! receive parameters
|
|
|
|
|
call igebr2d(icontxt,'ALL',' ',10,1,intbuf,10,0,0)
|
|
|
|
|
do i = 1, 10
|
|
|
|
|
cmethd(i:i) = achar(intbuf(i))
|
|
|
|
|
end do
|
|
|
|
|
call igebr2d(icontxt,'ALL',' ',10,1,intbuf,10,0,0)
|
|
|
|
|
do i = 1, 10
|
|
|
|
|
prec(i:i) = achar(intbuf(i))
|
|
|
|
|
end do
|
|
|
|
|
call igebr2d(icontxt,'ALL',' ',10,1,intbuf,10,0,0)
|
|
|
|
|
do i = 1, 5
|
|
|
|
|
afmt(i:i) = achar(intbuf(i))
|
|
|
|
|
end do
|
|
|
|
|
call igebr2d(icontxt,'ALL',' ',5,1,intbuf,5,0,0)
|
|
|
|
|
idim = intbuf(1)
|
|
|
|
|
istopc = intbuf(2)
|
|
|
|
|
itmax = intbuf(3)
|
|
|
|
|
itrace = intbuf(4)
|
|
|
|
|
ml = 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 tfqmr cgs'
|
|
|
|
|
write(iout,*)' prec : ilu diagsc 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 or 3 [1] '
|
|
|
|
|
write(iout,*)' itmax maximum number of iterations [500] '
|
|
|
|
|
write(iout,*)' itrace 0 (no tracing, default) or '
|
|
|
|
|
write(iout,*)' >= 0 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,t,desc_a,parts,icontxt,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_spmat_type
|
|
|
|
|
use psb_descriptor_type
|
|
|
|
|
use psb_tools_mod
|
|
|
|
|
use psb_methd_mod
|
|
|
|
|
implicit none
|
|
|
|
|
integer :: idim
|
|
|
|
|
integer, parameter :: nbmax=10
|
|
|
|
|
real(kind(1.d0)),pointer :: b(:),t(:)
|
|
|
|
|
type(psb_desc_type) :: desc_a
|
|
|
|
|
integer :: icontxt, 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(kind(1.d0)) :: zt(nbmax),glob_x,glob_y,glob_z
|
|
|
|
|
integer :: m,n,nnz,glob_row,j
|
|
|
|
|
type(psb_dspmat_type) :: row_mat
|
|
|
|
|
integer :: x,y,z,counter,ia,i,indx_owner
|
|
|
|
|
integer :: nprow,npcol,myprow,mypcol
|
|
|
|
|
integer :: element
|
|
|
|
|
integer :: nv, inv
|
|
|
|
|
integer, allocatable :: prv(:)
|
|
|
|
|
integer, pointer :: ierrv(:)
|
|
|
|
|
real(kind(1.d0)), pointer :: dwork(:)
|
|
|
|
|
integer,pointer :: iwork(:)
|
|
|
|
|
! deltah dimension of each grid cell
|
|
|
|
|
! deltat discretization time
|
|
|
|
|
real(kind(1.d0)) :: deltah
|
|
|
|
|
real(kind(1.d0)),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
|
|
|
|
|
real(kind(1.d0)) :: mpi_wtime, t1, t2, t3, tins
|
|
|
|
|
real(kind(1.d0)) :: a1, a2, a3, a4, b1, b2, b3
|
|
|
|
|
external mpi_wtime,a1, a2, a3, a4, b1, b2, b3
|
|
|
|
|
integer :: nb, ir1, ir2, ipr, err_act
|
|
|
|
|
logical :: own
|
|
|
|
|
! common area
|
|
|
|
|
|
|
|
|
|
character(len=20) :: name, ch_err
|
|
|
|
|
|
|
|
|
|
info = 0
|
|
|
|
|
name = 'create_matrix'
|
|
|
|
|
call psb_erractionsave(err_act)
|
|
|
|
|
|
|
|
|
|
call blacs_gridinfo(icontxt, nprow, npcol, myprow, mypcol)
|
|
|
|
|
|
|
|
|
|
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)/(nprow*npcol))
|
|
|
|
|
write(*,*) 'size: n ',n
|
|
|
|
|
call psb_dscall(n,n,parts,icontxt,desc_a,info)
|
|
|
|
|
write(*,*) 'allocating a : nnz',nnz, info
|
|
|
|
|
call psb_spalloc(a,desc_a,info,nnz=nnz)
|
|
|
|
|
! define rhs from boundary conditions; also build initial guess
|
|
|
|
|
write(*,*) 'allocating b', info
|
|
|
|
|
call psb_alloc(n,b,desc_a,info)
|
|
|
|
|
write(*,*) 'allocating t', info
|
|
|
|
|
call psb_alloc(n,t,desc_a,info)
|
|
|
|
|
if(info.ne.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.
|
|
|
|
|
!
|
|
|
|
|
row_mat%descra(1:1) = 'G'
|
|
|
|
|
row_mat%fida = 'CSR'
|
|
|
|
|
write(*,*) 'allocating row_mat',20*nbmax
|
|
|
|
|
allocate(row_mat%aspk(20*nbmax),row_mat%ia1(20*nbmax),&
|
|
|
|
|
&row_mat%ia2(20*nbmax),prv(nprow),stat=info)
|
|
|
|
|
if (info.ne.0 ) then
|
|
|
|
|
info=4000
|
|
|
|
|
call psb_errpush(info,name)
|
|
|
|
|
goto 9999
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
tins = 0.d0
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t1 = mpi_wtime()
|
|
|
|
|
|
|
|
|
|
! loop over rows belonging to current process in a block
|
|
|
|
|
! distribution.
|
|
|
|
|
|
|
|
|
|
row_mat%ia2(1)=1
|
|
|
|
|
do glob_row = 1, n
|
|
|
|
|
call parts(glob_row,n,nprow,prv,nv)
|
|
|
|
|
do inv = 1, nv
|
|
|
|
|
indx_owner = prv(inv)
|
|
|
|
|
if (indx_owner == myprow) then
|
|
|
|
|
! local matrix pointer
|
|
|
|
|
element=0
|
|
|
|
|
! compute gridpoint coordinates
|
|
|
|
|
if (mod(glob_row,(idim*idim)).eq.0) then
|
|
|
|
|
x = glob_row/(idim*idim)
|
|
|
|
|
else
|
|
|
|
|
x = glob_row/(idim*idim)+1
|
|
|
|
|
endif
|
|
|
|
|
if (mod((glob_row-(x-1)*idim*idim),idim).eq.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
|
|
|
|
|
if (x.eq.1) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else if (y.eq.1) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else if (z.eq.1) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else if (x.eq.idim) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else if (y.eq.idim) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else if (z.eq.idim) then
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=one
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
else
|
|
|
|
|
! internal point: build discretization
|
|
|
|
|
!
|
|
|
|
|
! term depending on (x-1,y,z)
|
|
|
|
|
!
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a1(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-2)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x,y-1,z)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a2(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-2)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x,y,z-1)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b3(glob_x,glob_y,glob_z)&
|
|
|
|
|
& -a3(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z-1)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x,y,z)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(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)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x,y,z+1)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z+1)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x,y+1,z)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x-1)*idim*idim+(y)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
! term depending on (x+1,y,z)
|
|
|
|
|
element=element+1
|
|
|
|
|
row_mat%aspk(element)=-b3(glob_x,glob_y,glob_z)
|
|
|
|
|
row_mat%aspk(element) = row_mat%aspk(element)/(deltah*&
|
|
|
|
|
& deltah)
|
|
|
|
|
row_mat%ia2(element)=(x)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
row_mat%ia1(element)=glob_row
|
|
|
|
|
endif
|
|
|
|
|
row_mat%m=1
|
|
|
|
|
row_mat%k=n
|
|
|
|
|
! row_mat%ia2(2)=element
|
|
|
|
|
! ia== global row index
|
|
|
|
|
ia=glob_row
|
|
|
|
|
!!$ ia=(x-1)*idim*idim+(y-1)*idim+(z)
|
|
|
|
|
!!$ write(0,*) 'inserting row ',ia,' on proc',myprow
|
|
|
|
|
t3 = mpi_wtime()
|
|
|
|
|
call psb_spins(element,row_mat%ia1,row_mat%ia2,row_mat%aspk,a,desc_a,info)
|
|
|
|
|
if(info.ne.0) exit
|
|
|
|
|
tins = tins + (mpi_wtime()-t3)
|
|
|
|
|
! build rhs
|
|
|
|
|
if (x==1) then
|
|
|
|
|
glob_y=(y-idim/2)*deltah
|
|
|
|
|
glob_z=(z-idim/2)*deltah
|
|
|
|
|
zt(1) = exp(-glob_y**2-glob_z**2)
|
|
|
|
|
else if ((y==1).or.(y==idim).or.(z==1).or.(z==idim)) then
|
|
|
|
|
glob_x=3*(x-1)*deltah
|
|
|
|
|
glob_y=(y-idim/2)*deltah
|
|
|
|
|
glob_z=(z-idim/2)*deltah
|
|
|
|
|
zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)
|
|
|
|
|
else
|
|
|
|
|
zt(1) = 0.d0
|
|
|
|
|
endif
|
|
|
|
|
call psb_ins(1,b,ia,zt(1:1),desc_a,info)
|
|
|
|
|
if(info.ne.0) exit
|
|
|
|
|
zt(1)=0.d0
|
|
|
|
|
call psb_ins(1,t,ia,zt(1:1),desc_a,info)
|
|
|
|
|
if(info.ne.0) exit
|
|
|
|
|
end if
|
|
|
|
|
end do
|
|
|
|
|
end do
|
|
|
|
|
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t2 = mpi_wtime()
|
|
|
|
|
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='insert rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
write(*,*) ' pspins time',tins
|
|
|
|
|
write(*,*) ' insert time',(t2-t1)
|
|
|
|
|
|
|
|
|
|
deallocate(row_mat%aspk,row_mat%ia1,row_mat%ia2)
|
|
|
|
|
|
|
|
|
|
write(*,*) 'calling spasb'
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t1 = mpi_wtime()
|
|
|
|
|
call psb_dscasb(desc_a,info)
|
|
|
|
|
call psb_spasb(a,desc_a,info,dup=1,afmt=afmt)
|
|
|
|
|
call blacs_barrier(icontxt,'ALL')
|
|
|
|
|
t2 = mpi_wtime()
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='asb rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
write(0,*) ' assembly time',(t2-t1),' ',a%fida(1:4)
|
|
|
|
|
|
|
|
|
|
call psb_asb(b,desc_a,info)
|
|
|
|
|
call psb_asb(t,desc_a,info)
|
|
|
|
|
if(info.ne.0) then
|
|
|
|
|
info=4010
|
|
|
|
|
ch_err='asb rout.'
|
|
|
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
|
|
|
goto 9999
|
|
|
|
|
end if
|
|
|
|
|
|
|
|
|
|
if (myprow.eq.0) then
|
|
|
|
|
write(0,*) ' end create_matrix'
|
|
|
|
|
endif
|
|
|
|
|
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
return
|
|
|
|
|
|
|
|
|
|
9999 continue
|
|
|
|
|
call psb_erractionrestore(err_act)
|
|
|
|
|
if (err_act.eq.act_abort) then
|
|
|
|
|
call psb_error(icontxt)
|
|
|
|
|
return
|
|
|
|
|
end if
|
|
|
|
|
return
|
|
|
|
|
end subroutine create_matrix
|
|
|
|
|
end program pde90
|
|
|
|
|
!
|
|
|
|
|
! functions parametrizing the differential equation
|
|
|
|
|
!
|
|
|
|
|
function a1(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a1
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a1=1.d0
|
|
|
|
|
end function a1
|
|
|
|
|
function a2(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a2
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a2=2.d1*y
|
|
|
|
|
end function a2
|
|
|
|
|
function a3(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a3
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a3=1.d0
|
|
|
|
|
end function a3
|
|
|
|
|
function a4(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: a4
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
a4=1.d0
|
|
|
|
|
end function a4
|
|
|
|
|
function b1(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b1
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b1=1.d0
|
|
|
|
|
end function b1
|
|
|
|
|
function b2(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b2
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b2=1.d0
|
|
|
|
|
end function b2
|
|
|
|
|
function b3(x,y,z)
|
|
|
|
|
real(kind(1.d0)) :: b3
|
|
|
|
|
real(kind(1.d0)) :: x,y,z
|
|
|
|
|
b3=1.d0
|
|
|
|
|
end function b3
|
|
|
|
|
|
|
|
|
|
|
