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amg4psblas/mlprec/mld_ziluk_fct.f90

943 lines
36 KiB
Fortran

!!$
!!$
!!$ MLD2P4
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS v.2.0)
!!$
!!$ (C) Copyright 2007 Alfredo Buttari University of Rome Tor Vergata
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$
!!$ 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
!!$ software without specific written permission.
!!$
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$
!!$
! File: mld_ziluk_fct.f90
!
! Subroutine: mld_ziluk_fct
! Version: complex
! Contains: mld_ziluk_fctint, iluk_copyin, iluk_fact, iluk_copyout
!
! This routine computes either the ILU(k) or the MILU(k) factorization of the
! local part of the matrix stored into a. These factorizations are 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 factorizations can be found in
! Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition,
! SIAM, 2003, Chapter 10.
!
! The local matrix to be factorized 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)/MILU(k) factorization).
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in level k in ILU(k)/MILU(k).
! ialg - integer, input.
! The type of incomplete factorization to be performed.
! The MILU(k) factorization is computed if ialg = 2 (= mld_milu_n_);
! the ILU(k) factorization otherwise.
! a - type(psb_zspmat_type), input.
! The sparse matrix structure containing the local matrix to be
! factorized. Note that if the 'base' Additive Schwarz preconditioner
! has overlap greater than 0 and the matrix has not been reordered
! (see mld_bjac_bld), then a contains only the 'original' local part
! of the matrix to be factorized, 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(kind(1.d0)), 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
! matrix to be factorized, that have been retrieved by mld_asmat_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_bjac_bld), then blck does not contain any row.
!
subroutine mld_ziluk_fct(fill_in,ialg,a,l,u,d,info,blck)
use psb_base_mod
use mld_prec_mod, mld_protect_name => mld_ziluk_fct
implicit none
! Arguments
integer, intent(in) :: fill_in, ialg
integer, intent(out) :: info
type(psb_zspmat_type),intent(in) :: a
type(psb_zspmat_type),intent(inout) :: l,u
type(psb_zspmat_type),intent(in), optional, target :: blck
complex(kind(1.d0)), intent(inout) :: d(:)
! Local Variables
integer :: l1, l2, m, err_act
type(psb_zspmat_type), pointer :: blck_
character(len=20) :: name, ch_err
name='mld_ziluk_fct'
info = 0
call psb_erractionsave(err_act)
!
! 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) or the MILU(k) factorization, depending on ialg
!
call mld_ziluk_fctint(fill_in,ialg,m,a%m,a,blck_%m,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_ziluk_fctint'
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_ziluk_fctint
! Version: complex
! Note: internal subroutine of mld_ziluk_fct
!
! This routine computes either the ILU(k) or the MILU(k) factorization of the
! local part of the matrix stored into a. These factorizations are 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)/MILU(k) factorization).
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in level k in ILU(k)/MILU(k).
! ialg - integer, input.
! The type of incomplete factorization to be performed.
! The MILU(k) factorization is computed if ialg = 2 (= mld_milu_n_);
! the ILU(k) factorization otherwise.
! m - integer, output.
! The total number of rows of the local matrix to be factorized,
! i.e. ma+mb.
! ma - integer, input.
! The number of rows of the local submatrix stored into a.
! a - type(psb_zspmat_type), input.
! The sparse matrix structure containing the local matrix to be
! factorized. Note that, if the 'base' Additive Schwarz preconditioner
! has overlap greater than 0 and the matrix has not been reordered
! (see mld_bjac_bld), then a contains only the 'original' local part
! of the matrix to be factorized, i.e. the rows of the matrix held
! by the calling process according to the initial data distribution.
! mb - integer, input.
! The number of rows of the local submatrix stored into b.
! b - type(psb_zspmat_type), input.
! The sparse matrix structure containing the remote rows of the
! matrix to be factorized, that have been retrieved by mld_asmat_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_bjac_bld), then b does not contain any row.
! d - complex(kind(1.d0)), dimension(:), output.
! The inverse of the diagonal entries of the U factor in the incomplete
! factorization.
! laspk - complex(kind(1.d0)), 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(kind(1.d0)), 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_ziluk_fctint(fill_in,ialg,m,ma,a,mb,b,&
& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
use psb_base_mod
implicit none
! Arguments
integer, intent(in) :: fill_in, ialg
type(psb_zspmat_type) :: a,b
integer :: m,ma,mb,l1,l2,info
integer, dimension(:), allocatable :: lia1,lia2,uia1,uia2
complex(kind(1.d0)), dimension(:), allocatable :: laspk,uaspk
complex(kind(1.d0)), dimension(:) :: d
! Local variables
integer :: i, ktrw,err_act, nidx
integer, allocatable :: uplevs(:), rowlevs(:),idxs(:)
complex(kind(1.d0)), allocatable :: row(:)
type(psb_int_heap) :: heap
logical,parameter :: debug=.false.
type(psb_zspmat_type) :: trw
character(len=20), parameter :: name='mld_ziluk_fctint'
character(len=20) :: ch_err
if (psb_get_errstatus() /= 0) return
info=0
call psb_erractionsave(err_act)
m = ma+mb
!
! Allocate a temporary buffer for the iluk_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 and the corresponding
! fill levels
!
allocate(uplevs(size(uaspk)),rowlevs(m),row(m),stat=info)
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
uplevs(:) = m+1
row(:) = zzero
rowlevs(:) = -(m+1)
!
! 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 iluk_copyin routine, and updated during the elimination, in
! the iluk_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
!
! Copy into trw the i-th local row of the matrix, stored in a
!
call iluk_copyin(i,ma,a,1,m,row,rowlevs,heap,ktrw,trw)
else
!
! Copy into trw the i-th local row of the matrix, stored in b
! (as (i-ma)-th row)
!
call iluk_copyin(i-ma,mb,b,1,m,row,rowlevs,heap,ktrw,trw)
endif
! Do an elimination step on the current row. It turns out we only
! need to keep track of fill levels for the upper triangle, hence we
! do not have a lowlevs variable.
!
call iluk_fact(fill_in,i,m,row,rowlevs,heap,&
& d,uia1,uia2,uaspk,uplevs,nidx,idxs)
!
! Copy the row into laspk/d(i)/uaspk
!
call iluk_copyout(fill_in,ialg,i,m,row,rowlevs,nidx,idxs,&
& l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk,uplevs)
end do
!
! And we're done, so deallocate the memory
!
deallocate(uplevs,rowlevs,row,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_ziluk_fctint
!
! Subroutine: iluk_copyin
! Version: complex
! Note: internal subroutine of mld_ziluk_fct
!
! This routine copies a row of a sparse matrix A, stored in the sparse matrix
! structure a, into the array row and stores into a heap the column indices of
! the nonzero entries of the copied 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 iluk_fact after the call
! to iluk_copyin (see mld_iluk_fctint).
! The routine also sets to zero the entries of the array rowlevs corresponding
! to the nonzero entries of the copied row (see the description of the arguments
! below).
!
! 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
! ilu_copyin.
!
! This routine is used by mld_ziluk_fctint in the computation of the
! ILU(k)/MILU(k) 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.
! 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).
! row - complex(kind(1.d0)), dimension(:), input/output.
! In input it is the null vector (see mld_iluk_fctint and
! iluk_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 iluk_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_dspmat_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 iluk_copyin(i,m,a,jmin,jmax,row,rowlevs,heap,ktrw,trw)
use psb_base_mod
implicit none
! Arguments
type(psb_zspmat_type) :: a,trw
integer :: i, rowlevs(:),m,ktrw,jmin,jmax
complex(kind(1.d0)) :: row(:)
type(psb_int_heap) :: heap
! Local variables
integer :: k,j,info,irb
integer, parameter :: nrb=16
character(len=20), parameter :: name='mld_ziluk_fctint'
character(len=20) :: ch_err
if (psb_get_errstatus() /= 0) return
info=0
call psb_erractionsave(err_act)
call psb_init_heap(heap,info)
if (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)
rowlevs(k) = 0
call psb_insert_heap(k,heap,info)
end if
end do
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 iluk_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
ch_err='psb_sp_getblk'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
ktrw=1
end if
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)
rowlevs(k) = 0
call psb_insert_heap(k,heap,info)
end if
ktrw = ktrw + 1
enddo
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 iluk_copyin
!
! Subroutine: iluk_fact
! Version: complex
! Note: internal subroutine of mld_ziluk_fct
!
! This routine does an elimination step of the ILU(k) factorization on a
! single matrix row (see the calling routine mld_iluk_fctint).
!
! This step is also the base for a MILU(k) elimination step on the row (see
! iluk_copyout). This routine is used by mld_ziluk_fctint in the computation
! of the ILU(k)/MILU(k) factorization of a local sparse matrix.
!
! NOTE: it turns out we only need to keep track of the fill levels for
! the upper triangle.
!
!
! Arguments
! fill_in - integer, input.
! The fill-in level k in ILU(k).
! i - integer, input.
! The local index of the row to which the factorization is
! applied.
! m - integer, input.
! The number of rows of the local matrix to which the row
! belongs.
! row - complex(kind(1.d0)), 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.
! rowlevs - integer, dimension(:), input/output.
! In input rowlevs(k) = 0 if the k-th entry of the row is
! nonzero, and rowlevs(k) = -(m+1) otherwise. In output
! rowlevs(k) contains the fill kevel of the k-th entry of
! the row after the current elimination step; rowlevs(k) = -(m+1)
! means that the k-th row entry is zero throughout the elimination
! step.
! 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 indices concerning the transformed row.
! d - complex(kind(1.d0)), input.
! The inverse of the diagonal entries of the part of the U factor
! above the current row (see iluk_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
! iluk_copyout, called by mld_ziluk_fctint), 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 iluk_copyout, called by mld_ziluk_fctint), according to
! the CSR storage format.
! uaspk - complex(kind(1.d0)), dimension(:), input.
! The entries of the U factor above the current row (except the
! diagonal ones), stored according to the CSR format.
! uplevs - integer, dimension(:), input.
! The fill levels of the nonzero entries in the part of the
! U factor above the current row.
! 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 iluk_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 iluk_copyout.
! Note: this argument is intent(inout) and not only intent(out)
! to retain its allocation, done by this routine.
!
subroutine iluk_fact(fill_in,i,m,row,rowlevs,heap,d,uia1,uia2,uaspk,uplevs,nidx,idxs)
use psb_base_mod
implicit none
! Arguments
type(psb_int_heap) :: heap
integer :: i,m, rowlevs(:),fill_in,nidx
integer, allocatable :: idxs(:)
integer :: uia1(:),uia2(:),uplevs(:)
complex(kind(1.d0)) :: row(:), uaspk(:),d(:)
! Local variables
integer :: k,j,lrwk,jj,info, lastk
complex(kind(1.d0)) :: rwk
if (.not.allocated(idxs)) then
allocate(idxs(200),stat=info)
endif
nidx = 0
lastk = -1
!
! Do while there are indices to be processed
!
do
call psb_heap_get_first(k,heap,info)
if (info < 0) exit
!
! Just in case an index has been put on the heap more than once.
!
if (k == lastk) cycle
lastk = k
nidx = nidx + 1
if (nidx>size(idxs)) then
call psb_realloc(nidx+psb_heap_resize,idxs,info)
end if
idxs(nidx) = k
if ((row(k) /= zzero).and.(rowlevs(k) <= fill_in).and.(k<i)) then
!
! Note: since U is scaled while copying it out (see iluk_copyout),
! we can use rwk in the update below
!
rwk = row(k)
row(k) = row(k) * d(k) ! d(k) == 1/a(k,k)
lrwk = rowlevs(k)
do jj=uia2(k),uia2(k+1)-1
j = uia1(jj)
if (j<=k) then
write(0,*) 'Error in accessing upper mat???',j,k,jj
endif
!
! Insert the index into the heap for further processing.
! The fill levels are initialized to a negative value. If we find
! one, it means that it is an as yet untouched index, so we need
! to insert it; otherwise it is already on the heap, there is no
! need to insert it more than once.
!
if (rowlevs(j)<0) then
call psb_insert_heap(j,heap,info)
rowlevs(j) = abs(rowlevs(j))
end if
!
! Update row(j) and the corresponding fill level
!
row(j) = row(j) - rwk * uaspk(jj)
rowlevs(j) = min(rowlevs(j),lrwk+uplevs(jj)+1)
end do
end if
end do
end subroutine iluk_fact
!
! Subroutine: iluk_copyout
! Version: complex
! Note: internal subroutine of mld_ziluk_fct
!
! This routine copies a matrix row, computed by iluk_fact by applying an
! elimination step of the ILU(k) factorization, into the arrays laspk, uaspk,
! d, corresponding to the L factor, the U factor and the diagonal of U,
! respectively.
!
! Note that
! - 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)/MILU(k) factorization;
! - if the MILU(k) factorization has been required (ialg == mld_milu_n_), the
! row entries discarded because their fill levels are too high are added to
! the diagonal entry of the row;
! - the row entries are stored in laspk and uaspk according to the CSR format;
! - the arrays row and rowlevs are re-initialized for future use in mld_iluk_fct
! (see also iluk_copyin and iluk_fact).
!
! This routine is used by mld_ziluk_fctint in the computation of the
! ILU(k)/MILU(k) factorization of a local sparse matrix.
!
!
! Arguments:
! fill_in - integer, input.
! The fill-in level k in ILU(k)/MILU(k).
! ialg - integer, input.
! The type of incomplete factorization considered. The MILU(k)
! factorization is computed if ialg = 2 (= mld_milu_n_); the
! ILU(k) factorization otherwise.
! 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.
! row - complex(kind(1.d0)), 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
! iluk_copyin in mld_iluk_fact).
! rowlevs - integer, dimension(:), input/output.
! In input rowlevs(k) contains the fill kevel of the k-th entry
! of the row to be copied. rowlevs(k) = -(m+1) indicates that
! this entry is zero; however, any rowlevs(k) = -(m+1) is not
! used by the routine. In output rowlevs(k) = -(m+1) for all k's
! (this is an inizialization for the next call to iluk_copyin
! in mld_iluk_factint).
! nidx - integer, input.
! The number of entries of the array row that have been examined
! during the elimination step carried out by the routine iluk_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
! iluk_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_ziluk_fctint), 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_ziluk_fctint), according to the CSR storage format.
! laspk - complex(kind(1.d0)), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! L factor are copied.
! d - complex(kind(1.d0)), 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_ziluk_fctint), 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(kind(1.d0)), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! U factor are copied.
! uplevs - integer, dimension(:), input.
! The fill levels of the nonzero entries in the part of the
! U factor above the current row.
!
subroutine iluk_copyout(fill_in,ialg,i,m,row,rowlevs,nidx,idxs,&
& l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk,uplevs)
use psb_base_mod
implicit none
! Arguments
integer :: fill_in,ialg,i, rowlevs(:),l1,l2,m,nidx,idxs(:)
integer, allocatable :: uia1(:),uia2(:), lia1(:),lia2(:),uplevs(:)
complex(kind(1.d0)),allocatable :: uaspk(:), laspk(:)
complex(kind(1.d0)) :: row(:), d(:)
! Local variables
integer :: j,isz,info,err_act,int_err(5),idxp
character(len=20), parameter :: name='mld_ziluk_fctint'
character(len=20) :: ch_err
if (psb_get_errstatus() /= 0) return
info=0
call psb_erractionsave(err_act)
d(i) = dzero
do idxp=1,nidx
j = idxs(idxp)
if (j<i) then
!
! Copy the lower part of the row
!
if (rowlevs(j) <= fill_in) then
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) = j
laspk(l1) = row(j)
else if (ialg == mld_milu_n_) then
!
! MILU(k): add discarded entries to the diagonal one
!
d(i) = d(i) + row(j)
end if
!
! Re-initialize row(j) and rowlevs(j)
!
row(j) = zzero
rowlevs(j) = -(m+1)
else if (j==i) then
!
! Copy the diagonal entry of the row and re-initialize
! row(j) and rowlevs(j)
!
d(i) = d(i) + row(i)
row(i) = zzero
rowlevs(i) = -(m+1)
else if (j>i) then
!
! Copy the upper part of the row
!
if (rowlevs(j) <= fill_in) then
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) call psb_realloc(isz,uplevs,info,pad=(m+1))
if (info /= 0) then
info=4010
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
end if
uia1(l2) = j
uaspk(l2) = row(j)
uplevs(l2) = rowlevs(j)
else if (ialg == mld_milu_n_) then
!
! MILU(k): add discarded entries to the diagonal one
!
d(i) = d(i) + row(j)
end if
!
! Re-initialize row(j) and rowlevs(j)
!
row(j) = zzero
rowlevs(j) = -(m+1)
end if
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
!
! Check the pivot size
!
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) = zone/d(i)
end if
!
! Scale the upper part
!
do j=uia2(i), uia2(i+1)-1
uaspk(j) = d(i)*uaspk(j)
end do
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 iluk_copyout
end subroutine mld_ziluk_fct