!!$
!!$ Parallel Sparse BLAS version 2.3.1
!!$ (C) Copyright 2006, 2007, 2008, 2009, 2010
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
!!$
!!$ 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 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
!
! with Dirichlet boundary conditions, on the unit cube 0<=x,y,z<=1.
!
! 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) = exp(-x^2-y^2-z^2)
!
! Note that if a1=a2=a3=a4=0., the PDE is the well-known Laplace equation.
!
program pdgen
use psb_base_mod
use psb_util_mod
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, flops, tflops, tt1, tt2, bdwdth
! sparse matrix and preconditioner
type(psb_dspmat_type) :: a
! descriptor
type(psb_desc_type) :: desc_a, desc_b
! dense matrices
type(psb_d_vect_type) :: xxv,bv, vtst
real(psb_dpk_), allocatable :: tst(:)
! blacs parameters
integer(psb_ipk_) :: ictxt, iam, np
! solver parameters
integer(psb_ipk_) :: iter, itmax,itrace, istopc, irst, nr
integer(psb_long_int_k_) :: amatsize, precsize, descsize, d2size, annz, nbytes
real(psb_dpk_) :: err, eps
integer(psb_ipk_), parameter :: times=10
! other variables
integer(psb_ipk_) :: info, i
character(len=20) :: name,ch_err
character(len=40) :: fname
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='pde90'
call psb_set_errverbosity(2)
!
! Hello world
!
if (iam == psb_root_) then
write(*,*) 'Welcome to PSBLAS version: ',psb_version_string_
write(*,*) 'This is the ',trim(name),' sample program'
end if
!
! get parameters
!
call get_parms(ictxt,afmt,idim)
!
! allocate and fill in the coefficient matrix, rhs and initial guess
!
call psb_barrier(ictxt)
t1 = psb_wtime()
call create_matrix(idim,a,bv,xxv,desc_a,ictxt,afmt,info)
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
if(info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='create_matrix'
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,'(" ")')
!!$ write(fname,'(a,i0,a)') 'pde-',idim,'.hb'
!!$ call hb_write(a,info,filename=fname,rhs=b,key='PDEGEN',mtitle='MLD2P4 pdegen Test matrix ')
!!$ write(fname,'(a,i2.2,a,i2.2,a)') 'amat-',iam,'-',np,'.mtx'
!!$ call a%print(fname)
!!$ call psb_cdprt(20+iam,desc_a,short=.false.)
!!$ call psb_cdcpy(desc_a,desc_b,info)
!!$ call psb_set_debug_level(9999)
call psb_cdbldext(a,desc_a,2,desc_b,info,extype=psb_ovt_asov_)
if (info /= 0) then
write(0,*) 'Error from bldext'
call psb_abort(ictxt)
end if
call xxv%set(done)
call psb_barrier(ictxt)
t1 = psb_wtime()
do i=1,times
call psb_spmm(done,a,xxv,dzero,bv,desc_a,info,'n')
end do
call psb_barrier(ictxt)
t2 = psb_wtime() - t1
call psb_amx(ictxt,t2)
! FIXME: cache flush needed here
call psb_barrier(ictxt)
tt1 = psb_wtime()
do i=1,times
call psb_spmm(done,a,xxv,dzero,bv,desc_a,info,'t')
end do
call psb_barrier(ictxt)
tt2 = psb_wtime() - tt1
call psb_amx(ictxt,tt2)
call psb_amx(ictxt,t2)
nr = desc_a%get_global_rows()
annz = a%get_nzeros()
amatsize = a%sizeof()
descsize = psb_sizeof(desc_a)
call psb_sum(ictxt,annz)
call psb_sum(ictxt,amatsize)
call psb_sum(ictxt,descsize)
if (iam == psb_root_) then
flops = 1.d1*2*annz
tflops=flops
write(psb_out_unit,'("Matrix: ell1 ",i0)') idim
write(psb_out_unit,'("Test on : ",i20," processors")') np
write(psb_out_unit,'("Size of matrix : ",i20," ")') nr
write(psb_out_unit,'("Number of nonzeros : ",i20," ")') annz
write(psb_out_unit,'("Memory occupation : ",i20," ")') amatsize
write(psb_out_unit,'("Number of flops (",i0," prod) : ",F20.0," ")') times,flops
flops = flops / (t2)
tflops = tflops / (tt2)
write(psb_out_unit,'("Time for ",i0," products (s) : ",F20.3)')times, t2
write(psb_out_unit,'("Time per product (ms) : ",F20.3)') t2*1.d3/(1.d0*times)
write(psb_out_unit,'("MFLOPS : ",F20.3)') flops/1.d6
write(psb_out_unit,'("Time for ",i0," products (s) (trans.): ",F20.3)') times,tt2
write(psb_out_unit,'("Time per product (ms) (trans.): ",F20.3)') tt2*1.d3/(1.d0*times)
write(psb_out_unit,'("MFLOPS (trans.): ",F20.3)') tflops/1.d6
!
! This computation is valid for CSR
!
nbytes = nr*(2*psb_sizeof_dp + psb_sizeof_int)+&
& annz*(psb_sizeof_dp + psb_sizeof_int)
bdwdth = times*nbytes/(t2*1.d6)
write(psb_out_unit,*)
write(psb_out_unit,'("MBYTES/S : ",F20.3)') bdwdth
bdwdth = times*nbytes/(tt2*1.d6)
write(psb_out_unit,'("MBYTES/S (trans): ",F20.3)') bdwdth
write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt()
write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize
write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt()
write(psb_out_unit,'("Storage type for DESC_B: ",a)') desc_b%indxmap%get_fmt()
end if
!!$ 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 PREC: ",i12)')precsize
!!$ write(psb_out_unit,'("Total memory occupation for DESC_A: ",i12)')descsize
!!$ write(psb_out_unit,'("Storage type for DESC_A: ",a)') desc_a%indxmap%get_fmt()
!!$ write(psb_out_unit,'("Storage type for DESC_B: ",a)') desc_b%indxmap%get_fmt()
!
! cleanup storage and exit
!
call psb_gefree(bv,desc_a,info)
call psb_gefree(xxv,desc_a,info)
call psb_spfree(a,desc_a,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,afmt,idim)
integer(psb_ipk_) :: ictxt
character(len=*) :: afmt
integer(psb_ipk_) :: idim
integer(psb_ipk_) :: np, iam
integer(psb_ipk_) :: intbuf(10), ip
call psb_info(ictxt, iam, np)
if (iam == 0) then
read(psb_inp_unit,*) afmt
read(psb_inp_unit,*) idim
endif
call psb_bcast(ictxt,afmt)
call psb_bcast(ictxt,idim)
if (iam == 0) then
write(psb_out_unit,'("Testing 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,'(" ")')
end if
return
end subroutine get_parms
!
! print an error message
!
subroutine pr_usage(iout)
integer(psb_ipk_) :: 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,bv,xxv,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
use psb_mat_mod
implicit none
integer(psb_ipk_) :: idim
integer(psb_ipk_), parameter :: nb=20
type(psb_d_vect_type) :: xxv,bv
type(psb_desc_type) :: desc_a
integer(psb_ipk_) :: ictxt, info
character :: afmt*5
type(psb_dspmat_type) :: a
type(psb_d_csc_sparse_mat) :: acsc
type(psb_d_coo_sparse_mat) :: acoo
type(psb_d_csr_sparse_mat) :: acsr
real(psb_dpk_) :: zt(nb),x,y,z
integer(psb_ipk_) :: m,n,nnz,glob_row,nlr,i,ii,ib,k
integer(psb_ipk_) :: ix,iy,iz,ia,indx_owner
integer(psb_ipk_) :: np, iam, nr, nt
integer(psb_ipk_) :: element
integer(psb_ipk_), allocatable :: irow(:),icol(:),myidx(:)
real(psb_dpk_), allocatable :: val(:)
! deltah dimension of each grid cell
! deltat discretization time
real(psb_dpk_) :: deltah, 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(psb_ipk_) :: err_act
character(len=20) :: name, ch_err,tmpfmt
info = psb_success_
name = 'create_matrix'
call psb_erractionsave(err_act)
call psb_info(ictxt, iam, np)
deltah = 1.d0/(idim-1)
deltah2 = deltah*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(xxv,desc_a,info)
if (info == psb_success_) call psb_geall(bv,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)/deltah2-a1(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*(-val(element))
else
val(element) = -b1(x,y,z)/deltah2-a1(x,y,z)/deltah
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)/deltah2-a2(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element) = -b2(x,y,z)/deltah2-a2(x,y,z)/deltah
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)/deltah2-a3(x,y,z)/deltah
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(x,y,z)/deltah2-a3(x,y,z)/deltah
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))/deltah2&
& + (a1(x,y,z) + a2(x,y,z) + a3(x,y,z)+ a4(x,y,z))/deltah
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)=-b1(x,y,z)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b1(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)/deltah2
zt(k) = exp(-x**2-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b2(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)=-b3(x,y,z)/deltah2
zt(k) = exp(-y**2-z**2)*exp(-x)*(-val(element))
else
val(element)=-b3(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),bv,desc_a,info)
if(info /= psb_success_) exit
zt(:)=0.d0
call psb_geins(ib,myidx(ii:ii+ib-1),zt(1:ib),xxv,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
if (info == psb_success_) call psb_geasb(xxv,desc_a,info)
if (info == psb_success_) call psb_geasb(bv,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
tmpfmt = a%get_fmt()
write(psb_out_unit,'("The matrix has been generated and assembled in ",a3," format.")')&
& tmpfmt
write(psb_out_unit,'("-allocation time : ",es12.5)') talc
write(psb_out_unit,'("-coeff. gen. time : ",es12.5)') tgen
write(psb_out_unit,'("-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
end if
return
end subroutine create_matrix
end program pdgen
!
! 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