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666 lines
20 KiB
Fortran
666 lines
20 KiB
Fortran
!!$
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!!$ Parallel Sparse BLAS version 2.2
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!!$ (C) Copyright 2006/2007/2008
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the PSBLAS group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! File: ppde.f90
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!
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! Program: ppde
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! This sample program shows how to build and solve a sparse linear
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!
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! The program solves a linear system based on the partial differential
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! equation
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!
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!
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!
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! The equation generated is
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!
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! b1 d d (u) b2 d d (u) a1 d (u)) a2 d (u)))
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! - ------ - ------ + ----- + ------ + a3 u = 0
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! dx dx dy dy dx dy
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!
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!
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! with Dirichlet boundary conditions on the unit cube
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!
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! 0<=x,y,z<=1
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!
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! The equation is discretized with finite differences and uniform stepsize;
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! the resulting discrete equation is
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!
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! ( u(x,y,z)(2b1+2b2+a1+a2)+u(x-1,y)(-b1-a1)+u(x,y-1)(-b2-a2)+
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! -u(x+1,y)b1-u(x,y+1)b2)*(1/h**2)
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!
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! Example taken from: C.T.Kelley
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! Iterative Methods for Linear and Nonlinear Equations
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! SIAM 1995
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!
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!
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! In this sample program the index space of the discretized
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! computational domain is first numbered sequentially in a standard way,
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! then the corresponding vector is distributed according to a BLOCK
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! data distribution.
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!
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! Boundary conditions are set in a very simple way, by adding
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! equations of the form
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!
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! u(x,y) = rhs(x,y)
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!
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program ppde
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use psb_base_mod
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use psb_prec_mod
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use psb_krylov_mod
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use psb_util_mod
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implicit none
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! input parameters
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character(len=20) :: kmethd, ptype
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character(len=5) :: afmt
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integer :: idim
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! miscellaneous
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real(kind(1.d0)), parameter :: one = 1.d0
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real(kind(1.d0)) :: t1, t2, tprec
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! sparse matrix and preconditioner
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type(psb_dspmat_type) :: a
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type(psb_dprec_type) :: prec
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! descriptor
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type(psb_desc_type) :: desc_a
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! dense matrices
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real(kind(1.d0)), allocatable :: b(:), x(:)
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! blacs parameters
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integer :: ictxt, iam, np
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! solver parameters
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integer :: iter, itmax,itrace, istopc, irst
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real(kind(1.d0)) :: err, eps
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! other variables
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integer :: info
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character(len=20) :: name,ch_err
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if(psb_get_errstatus() /= 0) goto 9999
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info=0
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name='pde90'
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call psb_set_errverbosity(2)
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call psb_set_erraction(0)
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call psb_init(ictxt)
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call psb_info(ictxt,iam,np)
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if (iam < 0) then
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! This should not happen, but just in case
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call psb_exit(ictxt)
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stop
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endif
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!
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! get parameters
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!
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call get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst)
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!
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! allocate and fill in the coefficient matrix, rhs and initial guess
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!
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call create_matrix(idim,a,b,x,desc_a,part_block,ictxt,afmt,info)
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t2 = psb_wtime() - t1
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if(info /= 0) then
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info=4010
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ch_err='create_matrix'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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call psb_amx(ictxt,t2)
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if (iam == psb_root_) write(*,'("Overall matrix creation time : ",es10.4)')t2
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if (iam == psb_root_) write(*,'(" ")')
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!
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! prepare the preconditioner.
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!
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if(iam == psb_root_) write(0,'("Setting preconditioner to : ",a)')ptype
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call psb_precinit(prec,ptype,info)
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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call psb_precbld(a,desc_a,prec,info)
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if(info /= 0) then
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info=4010
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ch_err='psb_precbld'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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tprec = psb_wtime()-t1
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call psb_amx(ictxt,tprec)
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if (iam == psb_root_) write(*,'("Preconditioner time : ",es10.4)')tprec
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if (iam == psb_root_) write(*,'(" ")')
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!
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! iterative method parameters
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!
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if(iam == psb_root_) write(*,'("Calling iterative method ",a)')kmethd
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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eps = 1.d-9
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call psb_krylov(kmethd,a,prec,b,x,eps,desc_a,info,&
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& itmax=itmax,iter=iter,err=err,itrace=itrace,istop=istopc,irst=irst)
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if(info /= 0) then
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info=4010
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ch_err='solver routine'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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call psb_barrier(ictxt)
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t2 = psb_wtime() - t1
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call psb_amx(ictxt,t2)
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if (iam == psb_root_) then
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write(*,'(" ")')
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write(*,'("Time to solve matrix : ",es10.4)')t2
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write(*,'("Time per iteration : ",es10.4)')t2/iter
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write(*,'("Number of iterations : ",i0)')iter
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write(*,'("Error estimate on exit : ",es10.4)')err
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write(*,'("Info on exit : ",i0)')info
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end if
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!
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! cleanup storage and exit
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!
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call psb_gefree(b,desc_a,info)
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call psb_gefree(x,desc_a,info)
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call psb_spfree(a,desc_a,info)
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call psb_precfree(prec,info)
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call psb_cdfree(desc_a,info)
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if(info /= 0) then
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info=4010
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ch_err='free routine'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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9999 continue
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if(info /= 0) then
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call psb_error(ictxt)
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end if
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call psb_exit(ictxt)
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stop
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contains
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!
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! get iteration parameters from the command line
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!
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subroutine get_parms(ictxt,kmethd,ptype,afmt,idim,istopc,itmax,itrace,irst)
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integer :: ictxt
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character(len=*) :: kmethd, ptype, afmt
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integer :: idim, istopc,itmax,itrace,irst
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integer :: np, iam
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integer :: intbuf(10), ip
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call psb_info(ictxt, iam, np)
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if (iam==0) then
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read(*,*) ip
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if (ip >= 3) then
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read(*,*) kmethd
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read(*,*) ptype
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read(*,*) afmt
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! broadcast parameters to all processors
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call psb_bcast(ictxt,kmethd)
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call psb_bcast(ictxt,afmt)
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call psb_bcast(ictxt,ptype)
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read(*,*) idim
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if (ip >= 4) then
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read(*,*) istopc
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else
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istopc=1
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endif
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if (ip >= 5) then
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read(*,*) itmax
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else
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itmax=500
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endif
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if (ip >= 6) then
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read(*,*) itrace
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else
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itrace=-1
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endif
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if (ip >= 7) then
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read(*,*) irst
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else
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irst=1
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endif
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! broadcast parameters to all processors
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intbuf(1) = idim
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intbuf(2) = istopc
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intbuf(3) = itmax
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intbuf(4) = itrace
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intbuf(5) = irst
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call psb_bcast(ictxt,intbuf(1:5))
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write(*,'("Solving matrix : ell1")')
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write(*,'("Grid dimensions : ",i4,"x",i4,"x",i4)')idim,idim,idim
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write(*,'("Number of processors : ",i0)')np
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write(*,'("Data distribution : BLOCK")')
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write(*,'("Preconditioner : ",a)') ptype
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write(*,'("Iterative method : ",a)') kmethd
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write(*,'(" ")')
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else
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! wrong number of parameter, print an error message and exit
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call pr_usage(0)
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call psb_abort(ictxt)
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stop 1
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endif
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else
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call psb_bcast(ictxt,kmethd)
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call psb_bcast(ictxt,afmt)
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call psb_bcast(ictxt,ptype)
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call psb_bcast(ictxt,intbuf(1:5))
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idim = intbuf(1)
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istopc = intbuf(2)
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itmax = intbuf(3)
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itrace = intbuf(4)
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irst = intbuf(5)
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end if
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return
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end subroutine get_parms
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!
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! print an error message
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!
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subroutine pr_usage(iout)
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integer :: iout
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write(iout,*)'incorrect parameter(s) found'
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write(iout,*)' usage: pde90 methd prec dim &
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&[istop itmax itrace]'
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write(iout,*)' where:'
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write(iout,*)' methd: cgstab cgs rgmres bicgstabl'
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write(iout,*)' prec : bjac diag none'
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write(iout,*)' dim number of points along each axis'
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write(iout,*)' the size of the resulting linear '
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write(iout,*)' system is dim**3'
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write(iout,*)' istop stopping criterion 1, 2 '
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write(iout,*)' itmax maximum number of iterations [500] '
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write(iout,*)' itrace <=0 (no tracing, default) or '
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write(iout,*)' >= 1 do tracing every itrace'
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write(iout,*)' iterations '
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end subroutine pr_usage
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!
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! subroutine to allocate and fill in the coefficient matrix and
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! the rhs.
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!
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subroutine create_matrix(idim,a,b,xv,desc_a,parts,ictxt,afmt,info)
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!
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! discretize the partial diferential equation
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!
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! b1 dd(u) b2 dd(u) b3 dd(u) a1 d(u) a2 d(u) a3 d(u)
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! - ------ - ------ - ------ - ----- - ------ - ------ + a4 u
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! dxdx dydy dzdz dx dy dz
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!
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! = 0
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!
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! boundary condition: dirichlet
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! 0< x,y,z<1
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!
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! u(x,y,z)(2b1+2b2+2b3+a1+a2+a3)+u(x-1,y,z)(-b1-a1)+u(x,y-1,z)(-b2-a2)+
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! + 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
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use psb_base_mod
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implicit none
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integer :: idim
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integer, parameter :: nbmax=10
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real(kind(1.d0)), allocatable :: b(:),xv(:)
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type(psb_desc_type) :: desc_a
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integer :: ictxt, info
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character :: afmt*5
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interface
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! .....user passed subroutine.....
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subroutine parts(global_indx,n,np,pv,nv)
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implicit none
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integer, intent(in) :: global_indx, n, np
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integer, intent(out) :: nv
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integer, intent(out) :: pv(*)
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end subroutine parts
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end interface ! local variables
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type(psb_dspmat_type) :: a
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real(kind(1.d0)) :: zt(nbmax),glob_x,glob_y,glob_z
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integer :: m,n,nnz,glob_row
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integer :: x,y,z,ia,indx_owner
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integer :: np, iam
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integer :: element
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integer :: nv, inv
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integer, allocatable :: irow(:),icol(:)
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real(kind(1.d0)), allocatable :: val(:)
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integer, allocatable :: prv(:)
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! deltah dimension of each grid cell
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! deltat discretization time
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real(kind(1.d0)) :: deltah
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real(kind(1.d0)),parameter :: rhs=0.d0,one=1.d0,zero=0.d0
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real(kind(1.d0)) :: t1, t2, t3, tins, tasb
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real(kind(1.d0)) :: a1, a2, a3, a4, b1, b2, b3
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external :: a1, a2, a3, a4, b1, b2, b3
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integer :: err_act
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! common area
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character(len=20) :: name, ch_err
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info = 0
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name = 'create_matrix'
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call psb_erractionsave(err_act)
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call psb_info(ictxt, iam, np)
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deltah = 1.d0/(idim-1)
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! initialize array descriptor and sparse matrix storage. provide an
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! estimate of the number of non zeroes
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m = idim*idim*idim
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n = m
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nnz = ((n*9)/(np))
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if(iam == psb_root_) write(0,'("Generating Matrix (size=",i0x,")...")')n
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call psb_cdall(ictxt,desc_a,info,mg=n,parts=parts)
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call psb_spall(a,desc_a,info,nnz=nnz)
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! define rhs from boundary conditions; also build initial guess
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call psb_geall(b,desc_a,info)
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call psb_geall(xv,desc_a,info)
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if(info /= 0) then
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info=4010
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ch_err='allocation rout.'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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! we build an auxiliary matrix consisting of one row at a
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! time; just a small matrix. might be extended to generate
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! a bunch of rows per call.
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!
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allocate(val(20*nbmax),irow(20*nbmax),&
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&icol(20*nbmax),prv(np),stat=info)
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if (info /= 0 ) then
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info=4000
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call psb_errpush(info,name)
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goto 9999
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endif
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tins = 0.d0
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call psb_barrier(ictxt)
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t1 = psb_wtime()
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! loop over rows belonging to current process in a block
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! distribution.
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! icol(1)=1
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do glob_row = 1, n
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call parts(glob_row,n,np,prv,nv)
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do inv = 1, nv
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indx_owner = prv(inv)
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if (indx_owner == iam) then
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! local matrix pointer
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element=1
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! compute gridpoint coordinates
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if (mod(glob_row,(idim*idim)) == 0) then
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x = glob_row/(idim*idim)
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else
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x = glob_row/(idim*idim)+1
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endif
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if (mod((glob_row-(x-1)*idim*idim),idim) == 0) then
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y = (glob_row-(x-1)*idim*idim)/idim
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else
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y = (glob_row-(x-1)*idim*idim)/idim+1
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endif
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z = glob_row-(x-1)*idim*idim-(y-1)*idim
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! glob_x, glob_y, glob_x coordinates
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glob_x=x*deltah
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glob_y=y*deltah
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glob_z=z*deltah
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! check on boundary points
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zt(1) = 0.d0
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! internal point: build discretization
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!
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! term depending on (x-1,y,z)
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!
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if (x==1) then
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val(element)=-b1(glob_x,glob_y,glob_z)&
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& -a1(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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zt(1) = exp(-glob_y**2-glob_z**2)*(-val(element))
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else
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val(element)=-b1(glob_x,glob_y,glob_z)&
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& -a1(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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icol(element)=(x-2)*idim*idim+(y-1)*idim+(z)
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element=element+1
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endif
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! term depending on (x,y-1,z)
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if (y==1) then
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val(element)=-b2(glob_x,glob_y,glob_z)&
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& -a2(glob_x,glob_y,glob_z)
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val(element) = val(element)/(deltah*&
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& deltah)
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|
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)
|
|
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
|
|
|
|
|