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673 lines
20 KiB
Fortran
673 lines
20 KiB
Fortran
!!$
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!!$
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!!$ MD2P4
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!!$ Multilevel Domain Decomposition Parallel Preconditioner Package for PSBLAS
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!!$ for
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!!$ Parallel Sparse BLAS v2.0
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!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari University of Rome Tor Vergata
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!!$ Daniela di Serafino Second University of Naples
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!!$ Pasqua D'Ambra ICAR-CNR
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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 MD2P4 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 MD2P4 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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subroutine mld_dilut_fct(fill_in,thres,ialg,a,l,u,d,info,blck)
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!
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! This routine copies and factors "on the fly" from A and BLCK
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! into L/D/U.
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!
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!
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use psb_base_mod
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use mld_prec_mod, mld_protect_name => mld_dilut_fct
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implicit none
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! .. Scalar Arguments ..
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integer, intent(in) :: fill_in, ialg
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real(kind(1.d0)), intent(in) :: thres
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integer, intent(out) :: info
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! .. Array Arguments ..
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type(psb_dspmat_type),intent(in) :: a
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type(psb_dspmat_type),intent(inout) :: l,u
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type(psb_dspmat_type),intent(in), optional, target :: blck
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real(kind(1.d0)), intent(inout) :: d(:)
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! .. Local Scalars ..
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integer :: l1, l2, m, err_act
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type(psb_dspmat_type), pointer :: blck_
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character(len=20) :: name, ch_err
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logical, parameter :: debug=.false.
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name='mld_dilut_fct'
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info = 0
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call psb_erractionsave(err_act)
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! .. Executable Statements ..
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!
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if (debug) write(0,*) 'mld_dilut_fct: start'
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if (present(blck)) then
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blck_ => blck
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else
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allocate(blck_,stat=info)
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if (info /= 0) then
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call psb_errpush(4010,name,a_err='Allocate')
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goto 9999
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end if
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call psb_sp_all(0,0,blck_,1,info)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_all'
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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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endif
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if (debug) write(0,*) 'mld_dilut_fct: calling fctint'
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call mld_dilut_fctint(fill_in,thres,ialg,m,a%m,a,blck_%m,blck_,&
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& d,l%aspk,l%ia1,l%ia2,u%aspk,u%ia1,u%ia2,l1,l2,info)
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if (info /= 0) then
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info=4010
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ch_err='mld_dilut_fctint'
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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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l%infoa(1) = l1
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l%fida = 'CSR'
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l%descra = 'TLU'
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u%infoa(1) = l2
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u%fida = 'CSR'
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u%descra = 'TUU'
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l%m = m
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l%k = m
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u%m = m
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u%k = m
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if (present(blck)) then
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blck_ => null()
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else
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call psb_sp_free(blck_,info)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_free'
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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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deallocate(blck_)
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endif
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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contains
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subroutine mld_dilut_fctint(fill_in,thres,ialg,m,ma,a,mb,b,&
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& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
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use psb_base_mod
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implicit none
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integer, intent(in) :: fill_in, ialg
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real(kind(1.d0)), intent(in) :: thres
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type(psb_dspmat_type) :: a,b
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integer :: m,ma,mb,l1,l2,info
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integer, dimension(:), allocatable :: lia1,lia2,uia1,uia2
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real(kind(1.d0)), dimension(:), allocatable :: laspk,uaspk
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real(kind(1.d0)), dimension(:) :: d
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integer :: i, ktrw,err_act,nidx,nlw,nup,jmaxup
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real(kind(1.d0)) :: nrmi
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integer, allocatable :: idxs(:)
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real(kind(1.d0)), allocatable :: row(:)
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type(psb_int_heap) :: heap
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logical,parameter :: debug=.false.
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type(psb_dspmat_type) :: trw
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character(len=20), parameter :: name='mld_dilut_fctint'
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character(len=20) :: ch_err
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if (psb_get_errstatus() /= 0) return
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info=0
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call psb_erractionsave(err_act)
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m = ma+mb
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!
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! Temp buffer for copyin function.
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!
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if (debug) write(0,*)'LUINT Allocating TRW'
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call psb_sp_all(0,0,trw,1,info)
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if (info==0) call psb_ensure_size(m+1,lia2,info)
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if (info==0) call psb_ensure_size(m+1,uia2,info)
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if (info /= 0) then
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info=4010
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call psb_errpush(info,name,a_err='psb_sp_all')
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goto 9999
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end if
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if (debug) write(0,*)'LUINT Done Allocating TRW'
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l1=0
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l2=0
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lia2(1) = 1
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uia2(1) = 1
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if (debug) write(0,*)'In DCSRLU Begin cycle',m,ma,mb
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! Initial allocation
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allocate(row(m),stat=info)
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if (info /= 0) then
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info=4010
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call psb_errpush(info,name,a_err='Allocate')
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goto 9999
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end if
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row(:) = dzero
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do i = 1, m
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if (debug) write(0,*)'LUINT: Loop index ',i
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!
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! At each iteration of the loop we keep the indices affected in a heap
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! initialized and filled in the copyin function, and updated during
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! the elimination. The heap is ideal because at each step we need the
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! lowest index, but we also need to insert new items, and the heap allows
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! to do both in log time.
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!
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d(i) = dzero
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if (i<=ma) then
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call ilut_copyin(i,ma,a,i,1,m,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw)
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else
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call ilut_copyin(i-ma,mb,b,i,1,m,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw)
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endif
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if (debug) write(0,*)'LUINT: input Copy done'
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!
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! Do an elimination step on current row
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!
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call ilut_fact(fill_in,thres,i,m,nrmi,row,heap,&
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& d,uia1,uia2,uaspk,nidx,idxs)
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!
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! Copy the row into the lower/diag/upper structures.
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!
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call ilut_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row,nidx,idxs,&
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& l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk)
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end do
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!
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! And we're done......hopefully :-)
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!
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deallocate(row,idxs,stat=info)
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if (info /= 0) then
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info=4010
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call psb_errpush(info,name,a_err='Deallocate')
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goto 9999
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end if
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if (info == 0) call psb_sp_free(trw,info)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_free'
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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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if (debug) write(0,*)'Leaving ilu_fct'
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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end subroutine mld_dilut_fctint
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subroutine ilut_copyin(i,m,a,jd,jmin,jmax,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw)
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use psb_base_mod
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implicit none
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type(psb_dspmat_type) :: a,trw
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integer :: i, m,ktrw,jmin,jmax,jd,nlw,nup,jmaxup
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real(kind(1.d0)) :: nrmi,row(:)
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type(psb_int_heap) :: heap
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integer :: k,j,info,irb,kin,nz
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integer, parameter :: nrb=16
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real(kind(1.d0)) :: dmaxup
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real(kind(1.d0)), external :: dnrm2
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character(len=20), parameter :: name='mld_dilut_fctint'
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character(len=20) :: ch_err
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if (psb_get_errstatus() /= 0) return
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info=0
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call psb_erractionsave(err_act)
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call psb_init_heap(heap,info)
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!
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! nrmi is the norm of the current sparse row.
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! For the time being, use the 2-norm.
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! Note: below the 2-norm includes also elements
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! that are outside [1..JMAX] strictly.
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! Is this really important?? TO BE CHECKED.
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!
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nlw = 0
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nup = 0
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jmaxup = 0
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dmaxup = dzero
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nrmi = dzero
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if (toupper(a%fida)=='CSR') then
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do j = a%ia2(i), a%ia2(i+1) - 1
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k = a%ia1(j)
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if ((jmin<=k).and.(k<=jmax)) then
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row(k) = a%aspk(j)
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call psb_insert_heap(k,heap,info)
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end if
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if (k<jd) nlw = nlw + 1
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if (k>jd) then
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nup = nup + 1
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if (abs(row(k))>dmaxup) then
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jmaxup = k
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dmaxup = abs(row(k))
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end if
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end if
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end do
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nz = a%ia2(i+1) - a%ia2(i)
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nrmi = dnrm2(nz,a%aspk(a%ia2(i)),ione)
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else
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if ((mod(i,nrb) == 1).or.(nrb==1)) then
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irb = min(m-i+1,nrb)
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call psb_sp_getblk(i,a,trw,info,lrw=i+irb-1)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_getblk'
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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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ktrw=1
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end if
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kin = ktrw
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do
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if (ktrw > trw%infoa(psb_nnz_)) exit
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if (trw%ia1(ktrw) > i) exit
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k = trw%ia2(ktrw)
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if ((jmin<=k).and.(k<=jmax)) then
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row(k) = trw%aspk(ktrw)
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call psb_insert_heap(k,heap,info)
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end if
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if (k<jd) nlw = nlw + 1
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if (k>jd) then
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nup = nup + 1
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if (abs(row(k))>dmaxup) then
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jmaxup = k
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dmaxup = abs(row(k))
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end if
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end if
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ktrw = ktrw + 1
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enddo
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nz = ktrw - kin
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nrmi = dnrm2(nz,trw%aspk(kin),ione)
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end if
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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end subroutine ilut_copyin
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subroutine ilut_fact(fill_in,thres,i,m,nrmi,row,heap,&
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& d,uia1,uia2,uaspk,nidx,idxs)
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use psb_base_mod
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implicit none
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type(psb_int_heap) :: heap
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integer :: i,m,fill_in,nidx
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real(kind(1.d0)), intent(in) :: thres,nrmi
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integer, allocatable :: idxs(:)
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integer :: uia1(:),uia2(:)
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real(kind(1.d0)) :: row(:), uaspk(:),d(:)
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integer :: k,j,jj,info, lastk
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real(kind(1.d0)) :: rwk
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logical, parameter :: debug=.false.
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! Do an elimination step on current row
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call psb_ensure_size(200,idxs,info)
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nidx = 0
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lastk = -1
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!
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! Do while there are indices to be processed
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!
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do
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call psb_heap_get_first(k,heap,info)
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if (info < 0) exit
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!
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! An index may have been put on the heap more than once.
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!
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if (k == lastk) cycle
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lastk = k
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lowert: if (k<i) then
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!
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! Dropping rule 1: compare row(k) with thres*2-norm of row
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!
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rwk = row(k)
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row(k) = row(k) * d(k)
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if (abs(row(k)) < thres*nrmi) then
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! drop the element
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row(k) = dzero
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! We just dropped this index, no need to insert it.
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cycle
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else
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! Note: since U is scaled while copying out, we can use rwk
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! in the update below
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!
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do jj=uia2(k),uia2(k+1)-1
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j = uia1(jj)
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if (j<=k) then
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write(0,*) 'Error in accessing upper mat???',j,k,jj
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endif
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!
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! Insert the index for further processing.
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! Is there a sensible way to prune the insertion?
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!
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row(j) = row(j) - rwk * uaspk(jj)
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if (abs(row(j)) < thres*nrmi) then
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! drop the element
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row(j) = dzero
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else
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call psb_insert_heap(j,heap,info)
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endif
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end do
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end if
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end if lowert
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!
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! If we get here it's an index we need to keep on copyout.
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!
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nidx = nidx + 1
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call psb_ensure_size(nidx,idxs,info,addsz=psb_heap_resize)
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idxs(nidx) = k
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end do
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if (debug) then
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write(0,*) 'At end of factint: ',i,nidx
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write(0,*) idxs(1:nidx)
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write(0,*) row(idxs(1:nidx))
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end if
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end subroutine ilut_fact
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subroutine ilut_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row, &
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& nidx,idxs,l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk)
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use psb_base_mod
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implicit none
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integer :: fill_in,i, l1,l2,m,nidx,idxs(:)
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integer :: nlw,nup,jmaxup
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integer, allocatable :: uia1(:),uia2(:), lia1(:),lia2(:)
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real(kind(1.d0)), intent(in) :: thres,nrmi
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real(kind(1.d0)),allocatable :: uaspk(:), laspk(:)
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real(kind(1.d0)) :: row(:), d(:)
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real(kind(1.d0)),allocatable :: xw(:)
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integer, allocatable :: xwid(:), indx(:)
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real(kind(1.d0)) :: witem
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integer :: widx
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integer :: k,isz,info,err_act,int_err(5),idxp, nz
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type(psb_double_idx_heap) :: heap
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character(len=20), parameter :: name='mld_dilut_fctint'
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character(len=20) :: ch_err
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logical :: fndmaxup
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logical, parameter :: debug=.false.
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if (psb_get_errstatus() /= 0) return
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info=0
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call psb_erractionsave(err_act)
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!
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! Copy the row into the lower/diag/upper structures.
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!
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!
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! Here we need to apply another dropping rule. We do it
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! by putting the nonzero elements in heaps, then copying
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! them out.
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!
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! The heap goes down on absolute value, so the first item
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! is the largest absolute value.
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!
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call psb_init_heap(heap,info,dir=psb_asort_down_)
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|
allocate(xwid(nidx),xw(nidx),indx(nidx))
|
|
|
|
|
|
! First the lower part.
|
|
nz = 0
|
|
idxp = 0
|
|
do
|
|
idxp = idxp + 1
|
|
if (idxp > nidx) exit
|
|
if (idxs(idxp) >= i) exit
|
|
widx = idxs(idxp)
|
|
witem = row(widx)
|
|
if (debug) then
|
|
write(0,*) 'Lower: Deciding on drop of item ',witem,widx,thres,nrmi,thres*nrmi
|
|
end if
|
|
! Dropping rule on 2-norm
|
|
if (abs(witem) < thres*nrmi) cycle
|
|
nz = nz + 1
|
|
xw(nz) = witem
|
|
xwid(nz) = widx
|
|
call psb_insert_heap(witem,widx,heap,info)
|
|
end do
|
|
! Now have to take out the first elements.
|
|
if (nz <= nlw+fill_in) then
|
|
! Just copy everything from xw, and it's already ordered
|
|
!!$ write(0,*) 'Lower triang copying everything ',i,nz
|
|
else
|
|
nz = nlw+fill_in
|
|
do k=1,nz
|
|
call psb_heap_get_first(witem,widx,heap,info)
|
|
xw(k) = witem
|
|
xwid(k) = widx
|
|
end do
|
|
end if
|
|
|
|
! Now put things back into ascending column order
|
|
call psb_msort(xwid(1:nz),indx(1:nz),dir=psb_sort_up_)
|
|
do k=1,nz
|
|
l1 = l1 + 1
|
|
if (size(laspk) < l1) then
|
|
! Figure out a good reallocation size!!
|
|
isz = (max((l1/i)*m,int(1.2*l1),l1+100))
|
|
call psb_realloc(isz,laspk,info)
|
|
if (info == 0) call psb_realloc(isz,lia1,info)
|
|
if (info /= 0) then
|
|
info=4010
|
|
call psb_errpush(info,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
end if
|
|
lia1(l1) = xwid(k)
|
|
laspk(l1) = xw(indx(k))
|
|
end do
|
|
|
|
!
|
|
! Make sure idxp now points to the diagonal element
|
|
!
|
|
if (idxp <= size(idxs)) then
|
|
if (idxs(idxp) < i) then
|
|
do
|
|
idxp = idxp + 1
|
|
if (idxp > nidx) exit
|
|
if (idxs(idxp) >= i) exit
|
|
end do
|
|
end if
|
|
end if
|
|
if (idxp > size(idxs)) then
|
|
write(0,*) 'Warning: missing diagonal element in the row '
|
|
else
|
|
if (idxs(idxp) > i) then
|
|
write(0,*) 'Warning: missing diagonal element in the row '
|
|
else if (idxs(idxp) /= i) then
|
|
write(0,*) 'Warning: impossible error: diagonal has vanished'
|
|
else
|
|
! Copy the diagonal
|
|
widx = idxs(idxp)
|
|
witem = row(widx)
|
|
d(i) = witem
|
|
if (abs(d(i)) < epstol) then
|
|
!
|
|
! Pivot too small: unstable factorization
|
|
!
|
|
info = 2
|
|
int_err(1) = i
|
|
write(ch_err,'(g20.10)') d(i)
|
|
call psb_errpush(info,name,i_err=int_err,a_err=ch_err)
|
|
goto 9999
|
|
else
|
|
d(i) = done/d(i)
|
|
end if
|
|
end if
|
|
end if
|
|
|
|
!
|
|
! Now for the upper part
|
|
!
|
|
call psb_init_heap(heap,info,dir=psb_asort_down_)
|
|
nz = 0
|
|
do
|
|
idxp = idxp + 1
|
|
if (idxp > nidx) exit
|
|
widx = idxs(idxp)
|
|
if (widx <= i) then
|
|
write(0,*) 'Warning: lower triangle in upper copy',widx,i,idxp,idxs(idxp)
|
|
cycle
|
|
end if
|
|
if (widx > m) then
|
|
write(0,*) 'Warning: impossible value',widx,i,idxp,idxs(idxp)
|
|
cycle
|
|
end if
|
|
witem = row(widx)
|
|
if (debug) then
|
|
write(0,*) 'Upper: Deciding on drop of item ',witem,widx,&
|
|
& jmaxup,thres,nrmi,thres*nrmi
|
|
end if
|
|
! Dropping rule on 2-norm. But keep the entry of jmaxup anyway
|
|
|
|
if ((widx /= jmaxup) .and. (abs(witem) < thres*nrmi)) then
|
|
cycle
|
|
end if
|
|
nz = nz + 1
|
|
xw(nz) = witem
|
|
xwid(nz) = widx
|
|
call psb_insert_heap(witem,widx,heap,info)
|
|
end do
|
|
|
|
if (debug) then
|
|
write(0,*) 'Row ',i,' copyout: after first round at upper:',nz,jmaxup
|
|
write(0,*) xwid(1:nz)
|
|
write(0,*) xw(1:nz)
|
|
write(0,*) 'Dumping heap'
|
|
call psb_dump_heap(0,heap,info)
|
|
end if
|
|
|
|
! Now have to take out the first elements. But
|
|
! make sure we include jmaxup
|
|
if (nz <= nup+fill_in) then
|
|
! Just copy everything from xw
|
|
fndmaxup=.true.
|
|
else
|
|
fndmaxup = .false.
|
|
nz = nup+fill_in
|
|
do k=1,nz
|
|
call psb_heap_get_first(witem,widx,heap,info)
|
|
xw(k) = witem
|
|
xwid(k) = widx
|
|
if (widx == jmaxup) fndmaxup=.true.
|
|
end do
|
|
end if
|
|
if ((i<jmaxup).and.(jmaxup<=m)) then
|
|
if (.not.fndmaxup) then
|
|
!
|
|
! Include element at jmaxup, if not already there.
|
|
! Put it in place of smallest coefficient
|
|
!
|
|
xw(nz) = row(jmaxup)
|
|
xwid(nz) = jmaxup
|
|
endif
|
|
end if
|
|
! Now put things back into ascending column order
|
|
call psb_msort(xwid(1:nz),indx(1:nz),dir=psb_sort_up_)
|
|
if (debug) then
|
|
write(0,*) 'Row ',i,' copyout: after sort at upper:',nz,jmaxup
|
|
write(0,*) xwid(1:nz)
|
|
write(0,*) xw(indx(1:nz))
|
|
end if
|
|
! Upper part
|
|
do k=1,nz
|
|
l2 = l2 + 1
|
|
if (size(uaspk) < l2) then
|
|
! Figure out a good reallocation size!!
|
|
isz = max((l2/i)*m,int(1.2*l2),l2+100)
|
|
call psb_realloc(isz,uaspk,info)
|
|
if (info == 0) call psb_realloc(isz,uia1,info)
|
|
if (info /= 0) then
|
|
info=4010
|
|
call psb_errpush(info,name,a_err='Allocate')
|
|
goto 9999
|
|
end if
|
|
end if
|
|
uia1(l2) = xwid(k)
|
|
uaspk(l2) = d(i)*xw(indx(k))
|
|
end do
|
|
|
|
do idxp=1,nidx
|
|
row(idxs(idxp)) = dzero
|
|
end do
|
|
|
|
lia2(i+1) = l1 + 1
|
|
uia2(i+1) = l2 + 1
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
|
|
end subroutine ilut_copyout
|
|
|
|
|
|
end subroutine mld_dilut_fct
|