!!$
!!$
!!$ MLD2P4 version 1.0
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 2.2)
!!$
!!$ (C) Copyright 2008
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari University of Rome Tor Vergata
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$
!!$ 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 MLD2P4 group or the names of its contributors may
!!$ not be used to endorse or promote products derived from this
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!!$
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!!$
! File: mld_zilut_fact.f90
!
! Subroutine: mld_zilut_fact
! Version: real
! Contains: mld_zilut_factint, ilut_copyin, ilut_fact, ilut_copyout
!
! This routine computes the ILU(k,t) factorization of the diagonal blocks of a
! distributed matrix. This factorization is used to build the 'base
! preconditioner' (block-Jacobi preconditioner/solver, Additive Schwarz
! preconditioner) corresponding to a certain level of a multilevel preconditioner.
!
! Details on the above factorization can be found in
! Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition,
! SIAM, 2003, Chapter 10.
!
! The local matrix is stored into a and blck, as specified in
! the description of the arguments below. The storage format for both the L and
! U factors is CSR. The diagonal of the U factor is stored separately (actually,
! the inverse of the diagonal entries is stored; this is then managed in the solve
! stage associated to the ILU(k,t) factorization).
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in parameter k in ILU(k,t).
! thres - integer, input.
! The threshold t, i.e. the drop tolerance, in ILU(k,t).
! a - type(psb_zspmat_type), input.
! The sparse matrix structure containing the local matrix.
! Note that if the 'base' Additive Schwarz preconditioner
! has overlap greater than 0 and the matrix has not been reordered
! (see mld_fact_bld), then a contains only the 'original' local part
! of the distributed matrix, i.e. the rows of the matrix held
! by the calling process according to the initial data distribution.
! l - type(psb_zspmat_type), input/output.
! The L factor in the incomplete factorization.
! Note: its allocation is managed by the calling routine mld_ilu_bld,
! hence it cannot be only intent(out).
! u - type(psb_zspmat_type), input/output.
! The U factor (except its diagonal) in the incomplete factorization.
! Note: its allocation is managed by the calling routine mld_ilu_bld,
! hence it cannot be only intent(out).
! d - complex(psb_dpk_), dimension(:), input/output.
! The inverse of the diagonal entries of the U factor in the incomplete
! factorization.
! Note: its allocation is managed by the calling routine mld_ilu_bld,
! hence it cannot be only intent(out).
! info - integer, output.
! Error code.
! blck - type(psb_zspmat_type), input, optional, target.
! The sparse matrix structure containing the remote rows of the
! distributed matrix, that have been retrieved by mld_as_bld
! to build an Additive Schwarz base preconditioner with overlap
! greater than 0. If the overlap is 0 or the matrix has been reordered
! (see mld_fact_bld), then blck does not contain any row.
!
subroutine mld_zilut_fact(fill_in,thres,a,l,u,d,info,blck)
use psb_base_mod
use mld_inner_mod, mld_protect_name => mld_zilut_fact
implicit none
! Arguments
integer, intent(in) :: fill_in
real(psb_dpk_), intent(in) :: thres
integer, intent(out) :: info
type(psb_zspmat_type),intent(in) :: a
type(psb_zspmat_type),intent(inout) :: l,u
complex(psb_dpk_), intent(inout) :: d(:)
type(psb_zspmat_type),intent(in), optional, target :: blck
! Local Variables
integer :: l1, l2, m, err_act
type(psb_zspmat_type), pointer :: blck_
character(len=20) :: name, ch_err
name='mld_zilut_fact'
info = 0
call psb_erractionsave(err_act)
if (fill_in < 0) then
info=35
call psb_errpush(info,name,i_err=(/1,fill_in,0,0,0/))
goto 9999
end if
!
! Point to / allocate memory for the incomplete factorization
!
if (present(blck)) then
blck_ => blck
else
allocate(blck_,stat=info)
if (info /= 0) then
call psb_errpush(4010,name,a_err='Allocate')
goto 9999
end if
call psb_sp_all(0,0,blck_,1,info)
if (info /= 0) then
info=4010
ch_err='psb_sp_all'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
endif
!
! Compute the ILU(k,t) factorization
!
call mld_zilut_factint(fill_in,thres,m,a,blck_,&
& d,l%aspk,l%ia1,l%ia2,u%aspk,u%ia1,u%ia2,l1,l2,info)
if (info /= 0) then
info=4010
ch_err='mld_zilut_factint'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
!
! Store information on the L and U sparse matrices
!
l%infoa(1) = l1
l%fida = 'CSR'
l%descra = 'TLU'
u%infoa(1) = l2
u%fida = 'CSR'
u%descra = 'TUU'
l%m = m
l%k = m
u%m = m
u%k = m
!
! Nullify the pointer / deallocate the memory
!
if (present(blck)) then
blck_ => null()
else
call psb_sp_free(blck_,info)
if (info /= 0) then
info=4010
ch_err='psb_sp_free'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
deallocate(blck_)
endif
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
return
contains
!
! Subroutine: mld_zilut_factint
! Version: real
! Note: internal subroutine of mld_zilut_fact
!
! This routine computes the ILU(k,t) factorization of the diagonal blocks of a
! distributed matrix. This factorization is used to build the 'base
! preconditioner' (block-Jacobi preconditioner/solver, Additive Schwarz
! preconditioner) corresponding to a certain level of a multilevel preconditioner.
!
! The local matrix to be factorized is stored into a and b, as specified in the
! description of the arguments below. The storage format for both the L and U
! factors is CSR. The diagonal of the U factor is stored separately (actually,
! the inverse of the diagonal entries is stored; this is then managed in the
! solve stage associated to the ILU(k,t) factorization).
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in parameter k in ILU(k,t).
! thres - integer, input.
! The threshold t, i.e. the drop tolerance, in ILU(k,t).
! m - integer, output.
! The total number of rows of the local matrix to be factorized,
! i.e. ma+mb.
! a - type(psb_zspmat_type), input.
! The sparse matrix structure containing the local matrix.
! Note that, if the 'base' Additive Schwarz preconditioner
! has overlap greater than 0 and the matrix has not been reordered
! (see mld_fact_bld), then a contains only the 'original' local part
! of the distributed matrix, i.e. the rows of the matrix held
! by the calling process according to the initial data distribution.
! b - type(psb_zspmat_type), input.
! The sparse matrix structure containing the remote rows of the
! distributed matrix, that have been retrieved by mld_as_bld
! to build an Additive Schwarz base preconditioner with overlap
! greater than 0. If the overlap is 0 or the matrix has been reordered
! (see mld_fact_bld), then b does not contain any row.
! d - complex(psb_dpk_), dimension(:), output.
! The inverse of the diagonal entries of the U factor in the incomplete
! factorization.
! laspk - complex(psb_dpk_), dimension(:), input/output.
! The L factor in the incomplete factorization.
! lia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the L factor,
! according to the CSR storage format.
! lia2 - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the L factor in laspk, according to the CSR storage format.
! uaspk - complex(psb_dpk_), dimension(:), input/output.
! The U factor in the incomplete factorization.
! The entries of U are stored according to the CSR format.
! uia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the U factor,
! according to the CSR storage format.
! uia2 - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the U factor in uaspk, according to the CSR storage format.
! l1 - integer, output
! The number of nonzero entries in laspk.
! l2 - integer, output
! The number of nonzero entries in uaspk.
! info - integer, output.
! Error code.
!
subroutine mld_zilut_factint(fill_in,thres,m,a,b,&
& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
use psb_base_mod
implicit none
! Arguments
integer, intent(in) :: fill_in
real(psb_dpk_), intent(in) :: thres
type(psb_zspmat_type), intent(in) :: a,b
integer, intent(inout) :: m,l1,l2,info
integer, allocatable, intent(inout) :: lia1(:),lia2(:),uia1(:),uia2(:)
complex(psb_dpk_), allocatable, intent(inout) :: laspk(:),uaspk(:)
complex(psb_dpk_), intent(inout) :: d(:)
! Local Variables
integer :: i, ktrw,err_act,nidx,nlw,nup,jmaxup, ma, mb
real(psb_dpk_) :: nrmi
integer, allocatable :: idxs(:)
complex(psb_dpk_), allocatable :: row(:)
type(psb_int_heap) :: heap
type(psb_zspmat_type) :: trw
character(len=20), parameter :: name='mld_zilut_factint'
character(len=20) :: ch_err
if (psb_get_errstatus() /= 0) return
info = 0
call psb_erractionsave(err_act)
ma = a%m
mb = b%m
m = ma+mb
!
! Allocate a temporary buffer for the ilut_copyin function
!
call psb_sp_all(0,0,trw,1,info)
if (info==0) call psb_ensure_size(m+1,lia2,info)
if (info==0) call psb_ensure_size(m+1,uia2,info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_sp_all')
goto 9999
end if
l1=0
l2=0
lia2(1) = 1
uia2(1) = 1
!
! Allocate memory to hold the entries of a row
!
allocate(row(m),stat=info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
row(:) = zzero
!
! Cycle over the matrix rows
!
do i = 1, m
!
! At each iteration of the loop we keep in a heap the column indices
! affected by the factorization. The heap is initialized and filled
! in the ilut_copyin function, and updated during the elimination, in
! the ilut_fact routine. The heap is ideal because at each step we need
! the lowest index, but we also need to insert new items, and the heap
! allows to do both in log time.
!
d(i) = zzero
if (i<=ma) then
call ilut_copyin(i,ma,a,i,1,m,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw,info)
else
call ilut_copyin(i-ma,mb,b,i,1,m,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw,info)
endif
!
! Do an elimination step on current row
!
if (info == 0) call ilut_fact(thres,i,nrmi,row,heap,&
& d,uia1,uia2,uaspk,nidx,idxs,info)
!
! Copy the row into laspk/d(i)/uaspk
!
if (info == 0) call ilut_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row,nidx,idxs,&
& l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk,info)
if (info /= 0) then
info=4001
call psb_errpush(info,name,a_err='Copy/factor loop')
goto 9999
end if
end do
!
! And we're done, so deallocate the memory
!
deallocate(row,idxs,stat=info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='Deallocate')
goto 9999
end if
if (info == 0) call psb_sp_free(trw,info)
if (info /= 0) then
info=4010
ch_err='psb_sp_free'
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.eq.psb_act_abort_) then
call psb_error()
return
end if
return
end subroutine mld_zilut_factint
!
! Subroutine: ilut_copyin
! Version: complex
! Note: internal subroutine of mld_zilut_fact
!
! This routine performs the following tasks:
! - copying a row of a sparse matrix A, stored in the sparse matrix structure a,
! into the array row;
! - storing into a heap the column indices of the nonzero entries of the copied
! row;
! - computing the column index of the first entry with maximum absolute value
! in the part of the row belonging to the upper triangle;
! - computing the 2-norm of the row.
! The output array row is such that it contains a full row of A, i.e. it contains
! also the zero entries of the row. This is useful for the elimination step
! performed by ilut_fact after the call to ilut_copyin (see mld_ilut_factint).
!
! If the sparse matrix is in CSR format, a 'straight' copy is performed;
! otherwise psb_sp_getblk is used to extract a block of rows, which is then
! copied, row by row, into the array row, through successive calls to
! ilut_copyin.
!
! This routine is used by mld_zilut_factint in the computation of the ILU(k,t)
! factorization of a local sparse matrix.
!
!
! Arguments:
! i - integer, input.
! The local index of the row to be extracted from the
! sparse matrix structure a.
! m - integer, input.
! The number of rows of the local matrix stored into a.
! a - type(psb_zspmat_type), input.
! The sparse matrix structure containing the row to be
! copied.
! jd - integer, input.
! The column index of the diagonal entry of the row to be
! copied.
! jmin - integer, input.
! The minimum valid column index.
! jmax - integer, input.
! The maximum valid column index.
! The output matrix will contain a clipped copy taken from
! a(1:m,jmin:jmax).
! nlw - integer, output.
! The number of nonzero entries in the part of the row
! belonging to the lower triangle of the matrix.
! nup - integer, output.
! The number of nonzero entries in the part of the row
! belonging to the upper triangle of the matrix.
! jmaxup - integer, output.
! The column index of the first entry with maximum absolute
! value in the part of the row belonging to the upper triangle
! nrmi - real(psb_dpk_), output.
! The 2-norm of the current row.
! row - complex(psb_dpk_), dimension(:), input/output.
! In input it is the null vector (see mld_ilut_factint and
! ilut_copyout). In output it contains the row extracted
! from the matrix A. It actually contains a full row, i.e.
! it contains also the zero entries of the row.
! rowlevs - integer, dimension(:), input/output.
! In input rowlevs(k) = -(m+1) for k=1,...,m. In output
! rowlevs(k) = 0 for 1 <= k <= jmax and A(i,k) /=0, for
! future use in ilut_fact.
! heap - type(psb_int_heap), input/output.
! The heap containing the column indices of the nonzero
! entries in the array row.
! Note: this argument is intent(inout) and not only intent(out)
! to retain its allocation, done by psb_init_heap inside this
! routine.
! ktrw - integer, input/output.
! The index identifying the last entry taken from the
! staging buffer trw. See below.
! trw - type(psb_zspmat_type), input/output.
! A staging buffer. If the matrix A is not in CSR format, we use
! the psb_sp_getblk routine and store its output in trw; when we
! need to call psb_sp_getblk we do it for a block of rows, and then
! we consume them from trw in successive calls to this routine,
! until we empty the buffer. Thus we will make a call to psb_sp_getblk
! every nrb calls to copyin. If A is in CSR format it is unused.
!
subroutine ilut_copyin(i,m,a,jd,jmin,jmax,nlw,nup,jmaxup,nrmi,row,heap,ktrw,trw,info)
use psb_base_mod
implicit none
type(psb_zspmat_type), intent(in) :: a
type(psb_zspmat_type), intent(inout) :: trw
integer, intent(in) :: i, m,jmin,jmax,jd
integer, intent(inout) :: ktrw,nlw,nup,jmaxup,info
real(psb_dpk_), intent(inout) :: nrmi
complex(psb_dpk_), intent(inout) :: row(:)
type(psb_int_heap), intent(inout) :: heap
integer :: k,j,irb,kin,nz
integer, parameter :: nrb=16
real(psb_dpk_) :: dmaxup
real(psb_dpk_), external :: dznrm2
character(len=20), parameter :: name='mld_zilut_factint'
if (psb_get_errstatus() /= 0) return
info = 0
call psb_erractionsave(err_act)
call psb_init_heap(heap,info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_init_heap')
goto 9999
end if
!
! nrmi is the norm of the current sparse row (for the time being,
! we use the 2-norm).
! NOTE: the 2-norm below includes also elements that are outside
! [jmin:jmax] strictly. Is this really important? TO BE CHECKED.
!
nlw = 0
nup = 0
jmaxup = 0
dmaxup = dzero
nrmi = dzero
if (psb_toupper(a%fida)=='CSR') then
!
! Take a fast shortcut if the matrix is stored in CSR format
!
do j = a%ia2(i), a%ia2(i+1) - 1
k = a%ia1(j)
if ((jmin<=k).and.(k<=jmax)) then
row(k) = a%aspk(j)
call psb_insert_heap(k,heap,info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end if
if (k<jd) nlw = nlw + 1
if (k>jd) then
nup = nup + 1
if (abs(row(k))>dmaxup) then
jmaxup = k
dmaxup = abs(row(k))
end if
end if
end do
nz = a%ia2(i+1) - a%ia2(i)
nrmi = dznrm2(nz,a%aspk(a%ia2(i)),ione)
else
!
! Otherwise use psb_sp_getblk, slower but able (in principle) of
! handling any format. In this case, a block of rows is extracted
! instead of a single row, for performance reasons, and these
! rows are copied one by one into the array row, through successive
! calls to ilut_copyin.
!
if ((mod(i,nrb) == 1).or.(nrb==1)) then
irb = min(m-i+1,nrb)
call psb_sp_getblk(i,a,trw,info,lrw=i+irb-1)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_sp_getblk')
goto 9999
end if
ktrw=1
end if
kin = ktrw
do
if (ktrw > trw%infoa(psb_nnz_)) exit
if (trw%ia1(ktrw) > i) exit
k = trw%ia2(ktrw)
if ((jmin<=k).and.(k<=jmax)) then
row(k) = trw%aspk(ktrw)
call psb_insert_heap(k,heap,info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end if
if (k<jd) nlw = nlw + 1
if (k>jd) then
nup = nup + 1
if (abs(row(k))>dmaxup) then
jmaxup = k
dmaxup = abs(row(k))
end if
end if
ktrw = ktrw + 1
enddo
nz = ktrw - kin
nrmi = dznrm2(nz,trw%aspk(kin),ione)
end if
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
return
end subroutine ilut_copyin
!
! Subroutine: ilut_fact
! Version: complex
! Note: internal subroutine of mld_zilut_fact
!
! This routine does an elimination step of the ILU(k,t) factorization on a single
! matrix row (see the calling routine mld_ilut_factint). Actually, only the dropping
! rule based on the threshold is applied here. The dropping rule based on the
! fill-in is applied by ilut_copyout.
!
! The routine is used by mld_zilut_factint in the computation of the ILU(k,t)
! factorization of a local sparse matrix.
!
!
! Arguments
! thres - integer, input.
! The threshold t, i.e. the drop tolerance, in ILU(k,t).
! i - integer, input.
! The local index of the row to which the factorization is applied.
! nrmi - real(psb_dpk_), input.
! The 2-norm of the row to which the elimination step has to be
! applied.
! row - complex(psb_dpk_), dimension(:), input/output.
! In input it contains the row to which the elimination step
! has to be applied. In output it contains the row after the
! elimination step. It actually contains a full row, i.e.
! it contains also the zero entries of the row.
! heap - type(psb_int_heap), input/output.
! The heap containing the column indices of the nonzero entries
! in the processed row. In input it contains the indices concerning
! the row before the elimination step, while in output it contains
! the previous indices plus the ones corresponding to transformed
! entries in the 'upper part' that have not been dropped.
! d - complex(psb_dpk_), input.
! The inverse of the diagonal entries of the part of the U factor
! above the current row (see ilut_copyout).
! uia1 - integer, dimension(:), input.
! The column indices of the nonzero entries of the part of the U
! factor above the current row, stored in uaspk row by row (see
! ilut_copyout, called by mld_zilut_factint), according to the CSR
! storage format.
! uia2 - integer, dimension(:), input.
! The indices identifying the first nonzero entry of each row of
! the U factor above the current row, stored in uaspk row by row
! (see ilut_copyout, called by mld_zilut_factint), according to
! the CSR storage format.
! uaspk - complex(psb_dpk_), dimension(:), input.
! The entries of the U factor above the current row (except the
! diagonal ones), stored according to the CSR format.
! nidx - integer, output.
! The number of entries of the array row that have been
! examined during the elimination step. This will be used
! by the routine ilut_copyout.
! idxs - integer, dimension(:), allocatable, input/output.
! The indices of the entries of the array row that have been
! examined during the elimination step.This will be used by
! by the routine ilut_copyout.
! Note: this argument is intent(inout) and not only intent(out)
! to retain its allocation, done by this routine.
!
subroutine ilut_fact(thres,i,nrmi,row,heap,d,uia1,uia2,uaspk,nidx,idxs,info)
use psb_base_mod
implicit none
! Arguments
type(psb_int_heap), intent(inout) :: heap
integer, intent(in) :: i
integer, intent(inout) :: nidx,info
real(psb_dpk_), intent(in) :: thres,nrmi
integer, allocatable, intent(inout) :: idxs(:)
integer, intent(inout) :: uia1(:),uia2(:)
complex(psb_dpk_), intent(inout) :: row(:), uaspk(:),d(:)
! Local Variables
integer :: k,j,jj,lastk, iret
complex(psb_dpk_) :: rwk
info = 0
call psb_ensure_size(200,idxs,info)
if (info /= 0) return
nidx = 0
lastk = -1
!
! Do while there are indices to be processed
!
do
call psb_heap_get_first(k,heap,iret)
if (iret < 0) exit
!
! An index may have been put on the heap more than once.
!
if (k == lastk) cycle
lastk = k
lowert: if (k<i) then
!
! Dropping rule based on the threshold: compare the absolute
! value of each updated entry of row with thres * 2-norm of row.
!
rwk = row(k)
row(k) = row(k) * d(k)
if (abs(row(k)) < thres*nrmi) then
!
! Drop the entry.
!
row(k) = zzero
cycle
else
!
! Note: since U is scaled while copying it out (see ilut_copyout),
! we can use rwk in the update below.
!
do jj=uia2(k),uia2(k+1)-1
j = uia1(jj)
if (j<=k) then
info = -i
return
endif
!
! Update row(j) and, if it is not to be discarded, insert
! its index into the heap for further processing.
!
row(j) = row(j) - rwk * uaspk(jj)
if (abs(row(j)) < thres*nrmi) then
!
! Drop the entry.
!
row(j) = zzero
else
!
! Do the insertion.
!
call psb_insert_heap(j,heap,info)
if (info /= 0) return
endif
end do
end if
end if lowert
!
! If we get here it is an index we need to keep on copyout.
!
nidx = nidx + 1
call psb_ensure_size(nidx,idxs,info,addsz=psb_heap_resize)
if (info /= 0) return
idxs(nidx) = k
end do
end subroutine ilut_fact
!
! Subroutine: ilut_copyout
! Version: complex
! Note: internal subroutine of mld_zilut_fact
!
! This routine copies a matrix row, computed by ilut_fact by applying an
! elimination step of the ILU(k,t) factorization, into the arrays laspk,
! uaspk, d, corresponding to the L factor, the U factor and the diagonal
! of U, respectively.
!
! Note that
! - the dropping rule based on the fill-in is applied here and not in ilut_fact;
! it consists in keeping the nlw+k entries with largest absolute value in
! the 'lower part' of the row, and the nup+k ones in the 'upper part';
! - the entry in the upper part of the row which has maximum absolute value
! in the original matrix is included in the above nup+k entries anyway;
! - the part of the row stored into uaspk is scaled by the corresponding
! diagonal entry, according to the LDU form of the incomplete factorization;
! - the inverse of the diagonal entries of U is actually stored into d; this
! is then managed in the solve stage associated to the ILU(k,t) factorization;
! - the row entries are stored in laspk and uaspk according to the CSR format;
! - the array row is re-initialized for future use in mld_ilut_fact(see also
! ilut_copyin and ilut_fact).
!
! This routine is used by mld_zilut_factint in the computation of the ILU(k,t)
! factorization of a local sparse matrix.
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in parameter k in ILU(k,t).
! thres - integer, input.
! The threshold t, i.e. the drop tolerance, in ILU(k,t).
! i - integer, input.
! The local index of the row to be copied.
! m - integer, input.
! The number of rows of the local matrix under factorization.
! nlw - integer, input.
! The number of nonzero entries of the 'lower part' of the row
! in the initial matrix (i.e. the matrix before the factorization).
! nup - integer, input.
! The number of nonzero entries in the 'upper part' of the row
! in the initial matrix.
! jmaxup - integer, input.
! The column index of the first entry with maximum absolute
! value in the 'upper part' of the row in the initial matrix.
! nrmi - real(psb_dpk_), input.
! The 2-norm of the current row in the initial matrix.
! row - complex(psb_dpk_), dimension(:), input/output.
! It contains, input, the row to be copied, and, in output,
! the null vector (the latter is used in the next call to
! ilut_copyin in mld_ilut_fact).
! nidx - integer, input.
! The number of entries of the array row that have been examined
! during the elimination step carried out by the routine ilut_fact.
! idxs - integer, dimension(:), allocatable, input.
! The indices of the entries of the array row that have been
! examined during the elimination step carried out by the routine
! ilut_fact.
! l1 - integer, input/output.
! Pointer to the last occupied entry of laspk.
! l2 - integer, input/output.
! Pointer to the last occupied entry of uaspk.
! lia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the L factor,
! copied in laspk row by row (see mld_zilut_factint), according
! to the CSR storage format.
! lia2 - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the L factor, copied in laspk row by row (see
! mld_zilut_factint), according to the CSR storage format.
! laspk - complex(psb_dpk_), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! L factor are copied.
! d - complex(psb_dpk_), dimension(:), input/output.
! The array where the inverse of the diagonal entry of the
! row is copied (only d(i) is used by the routine).
! uia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the U factor
! copied in uaspk row by row (see mld_zilut_factint), according
! to the CSR storage format.
! uia2 - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the U factor copied in uaspk row by row (see
! mld_zilu_fctint), according to the CSR storage format.
! uaspk - complex(psb_dpk_), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! U factor are copied.
!
subroutine ilut_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row, &
& nidx,idxs,l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk,info)
use psb_base_mod
implicit none
! Arguments
integer, intent(in) :: fill_in,i,m,nidx,nlw,nup,jmaxup
integer, intent(in) :: idxs(:)
integer, intent(inout) :: l1,l2, info
integer, allocatable, intent(inout) :: uia1(:),uia2(:), lia1(:),lia2(:)
real(psb_dpk_), intent(in) :: thres,nrmi
complex(psb_dpk_),allocatable, intent(inout) :: uaspk(:), laspk(:)
complex(psb_dpk_), intent(inout) :: row(:), d(:)
! Local variables
complex(psb_dpk_),allocatable :: xw(:)
integer, allocatable :: xwid(:), indx(:)
complex(psb_dpk_) :: witem
integer :: widx
integer :: k,isz,err_act,int_err(5),idxp, nz
type(psb_dcomplex_idx_heap) :: heap
character(len=20), parameter :: name='ilut_copyout'
character(len=20) :: ch_err
logical :: fndmaxup
if (psb_get_errstatus() /= 0) return
info=0
call psb_erractionsave(err_act)
!
! Here we need to apply also the dropping rule base on the fill-in.
! We do it by putting into a heap the elements that are not dropped
! by using the 2-norm rule, and then copying them out.
!
! The heap goes down on the entry absolute value, so the first item
! is the largest absolute value.
!
call psb_init_heap(heap,info,dir=psb_asort_down_)
if (info == 0) allocate(xwid(nidx),xw(nidx),indx(nidx),stat=info)
if (info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/3*nidx,0,0,0,0/),&
& a_err='complex(psb_dpk_)')
goto 9999
end if
!
! 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)
!
! Dropping rule based on the 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)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end do
!
! Now we have to take out the first nlw+fill_in entries
!
if (nz <= nlw+fill_in) then
!
! Just copy everything from xw, and it is already ordered
!
else
nz = nlw+fill_in
do k=1,nz
call psb_heap_get_first(witem,widx,heap,info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_heap_get_first')
goto 9999
end if
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_)
!
! Copy out the lower part of the row
!
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 points to the diagonal entry
!
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 entry
!
widx = idxs(idxp)
witem = row(widx)
d(i) = witem
if (abs(d(i)) < epstol) then
!
! Too small pivot: 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
!
! Compute 1/pivot
!
d(i) = done/d(i)
end if
end if
end if
!
! Now the upper part
!
call psb_init_heap(heap,info,dir=psb_asort_down_)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_init_heap')
goto 9999
end if
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)
!
! Dropping rule based on the 2-norm. But keep the jmaxup-th entry 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)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end do
!
! Now we have to take out the first nup-fill_in entries. But make sure
! we include entry 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 entry jmaxup, if it is not already there.
! Put it in the place of the smallest coefficient.
!
xw(nz) = row(jmaxup)
xwid(nz) = jmaxup
endif
end if
!
! Now we put things back into ascending column order
!
call psb_msort(xwid(1:nz),indx(1:nz),dir=psb_sort_up_)
!
! Copy out the upper part of the row
!
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
!
! Set row to zero
!
do idxp=1,nidx
row(idxs(idxp)) = zzero
end do
!
! Store the pointers to the first non occupied entry of in
! laspk and uaspk
!
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_zilut_fact