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psblas3/prec/impl/psb_c_iluk_fact.f90

1015 lines
39 KiB
Fortran

!
! Parallel Sparse BLAS version 3.5
! (C) Copyright 2006-2018
! Salvatore Filippone
! Alfredo Buttari
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions
! are met:
! 1. Redistributions of source code must retain the above copyright
! notice, this list of conditions and the following disclaimer.
! 2. Redistributions in binary form must reproduce the above copyright
! notice, this list of conditions, and the following disclaimer in the
! documentation and/or other materials provided with the distribution.
! 3. The name of the PSBLAS group or the names of its contributors may
! not be used to endorse or promote products derived from this
! software without specific written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
! ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
! POSSIBILITY OF SUCH DAMAGE.
!
! Moved here from MLD2P4, original copyright below.
!
!
!
! MLD2P4 version 2.2
! MultiLevel Domain Decomposition Parallel Preconditioners Package
! based on PSBLAS (Parallel Sparse BLAS version 3.5)
!
! (C) Copyright 2008-2018
!
! Salvatore Filippone
! Pasqua D'Ambra
! Daniela di Serafino
!
! 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
! TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
! CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
! SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
! INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
! CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
! POSSIBILITY OF SUCH DAMAGE.
!
!
! File: psb_ciluk_fact.f90
!
! Subroutine: psb_ciluk_fact
! Version: complex
! Contains: psb_ciluk_factint, iluk_copyin, iluk_fact, iluk_copyout.
!
! This routine computes either the ILU(k) or the MILU(k) factorization of the
! diagonal blocks of a distributed matrix. 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 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 ILU(k) factorization is computed if ialg = 1 (= psb_ilu_n_);
! the MILU(k) one if ialg = 2 (= psb_milu_n_); other values are
! not allowed.
! a - type(psb_cspmat_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 psb_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_cspmat_type), input/output.
! The L factor in the incomplete factorization.
! Note: its allocation is managed by the calling routine psb_ilu_bld,
! hence it cannot be only intent(out).
! u - type(psb_cspmat_type), input/output.
! The U factor (except its diagonal) in the incomplete factorization.
! Note: its allocation is managed by the calling routine psb_ilu_bld,
! hence it cannot be only intent(out).
! d - complex(psb_spk_), 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 psb_ilu_bld,
! hence it cannot be only intent(out).
! info - integer, output.
! Error code.
! blck - type(psb_cspmat_type), input, optional, target.
! The sparse matrix structure containing the remote rows of the
! distributed matrix, that have been retrieved by psb_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 psb_fact_bld), then blck does not contain any row.
!
subroutine psb_ciluk_fact(fill_in,ialg,a,l,u,d,info,blck,shft)
use psb_base_mod
use psb_c_ilu_fact_mod, psb_protect_name => psb_ciluk_fact
implicit none
! Arguments
integer(psb_ipk_), intent(in) :: fill_in, ialg
integer(psb_ipk_), intent(out) :: info
type(psb_cspmat_type),intent(in) :: a
type(psb_cspmat_type),intent(inout) :: l,u
type(psb_cspmat_type),intent(in), optional, target :: blck
complex(psb_spk_), intent(inout) :: d(:)
complex(psb_spk_), intent(in), optional :: shft
! Local Variables
integer(psb_ipk_) :: l1, l2, m, err_act
complex(psb_spk_) :: shft_
type(psb_cspmat_type), pointer :: blck_
type(psb_c_csr_sparse_mat) :: ll, uu
character(len=20) :: name, ch_err
name='psb_ciluk_fact'
info = psb_success_
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 == psb_success_) call blck_%allocate(izero,izero,info,ione,type='CSR')
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='allocate'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
endif
if (present(shft)) then
shft_ = shft
else
shft_ = czero
end if
m = a%get_nrows() + blck_%get_nrows()
if ((m /= l%get_nrows()).or.(m /= u%get_nrows()).or.&
& (m > size(d)) ) then
write(0,*) 'Wrong allocation status for L,D,U? ',&
& l%get_nrows(),size(d),u%get_nrows()
info = -1
return
end if
call l%mv_to(ll)
call u%mv_to(uu)
!
! Compute the ILU(k) or the MILU(k) factorization, depending on ialg
!
call psb_ciluk_factint(fill_in,ialg,a,blck_,&
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,info,shft_)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='psb_ciluk_factint'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
!
! Store information on the L and U sparse matrices
!
call l%mv_from(ll)
call l%set_triangle()
call l%set_unit()
call l%set_lower()
call u%mv_from(uu)
call u%set_triangle()
call u%set_unit()
call u%set_upper()
!
! Nullify pointer / deallocate memory
!
if (present(blck)) then
blck_ => null()
else
call blck_%free()
deallocate(blck_,stat=info)
if(info.ne.0) then
info=psb_err_from_subroutine_
ch_err='psb_sp_free'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
endif
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
contains
!
! Subroutine: psb_ciluk_factint
! Version: complex
! Note: internal subroutine of psb_ciluk_fact
!
! This routine computes either the ILU(k) or the MILU(k) factorization of the
! diagonal blocks of a distributed matrix. 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 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 (= psb_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.
! a - type(psb_cspmat_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 psb_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_cspmat_type), input.
! The sparse matrix structure containing the remote rows of the
! distributed matrix, that have been retrieved by psb_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 psb_fact_bld), then b does not contain any row.
! d - complex(psb_spk_), dimension(:), output.
! The inverse of the diagonal entries of the U factor in the incomplete
! factorization.
! laspk - complex(psb_spk_), 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.
! uval - complex(psb_spk_), dimension(:), input/output.
! The U factor in the incomplete factorization.
! The entries of U are stored according to the CSR format.
! uja - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the U factor,
! according to the CSR storage format.
! uirp - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the U factor in uval, 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 uval.
! info - integer, output.
! Error code.
!
subroutine psb_ciluk_factint(fill_in,ialg,a,b,&
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,info,shft)
use psb_base_mod
implicit none
! Arguments
integer(psb_ipk_), intent(in) :: fill_in, ialg
type(psb_cspmat_type),intent(in) :: a,b
integer(psb_ipk_),intent(inout) :: l1,l2,info
integer(psb_ipk_), allocatable, intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
complex(psb_spk_), allocatable, intent(inout) :: lval(:),uval(:)
complex(psb_spk_), intent(inout) :: d(:)
complex(psb_spk_), intent(in) :: shft
! Local variables
integer(psb_ipk_) :: ma,mb,i, ktrw,err_act,nidx, m
integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:)
complex(psb_spk_), allocatable :: row(:)
type(psb_i_heap) :: heap
type(psb_c_coo_sparse_mat) :: trw
character(len=20), parameter :: name='psb_ciluk_factint'
character(len=20) :: ch_err
info=psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
select case(ialg)
case(psb_ilu_n_,psb_milu_n_)
! Ok
case default
info=psb_err_input_asize_invalid_i_
call psb_errpush(info,name,&
& i_err=(/itwo,ialg,izero,izero,izero/))
goto 9999
end select
if (fill_in < 0) then
info=psb_err_input_asize_invalid_i_
call psb_errpush(info,name, &
& i_err=(/ione,fill_in,izero,izero,izero/))
goto 9999
end if
ma = a%get_nrows()
mb = b%get_nrows()
m = ma+mb
!
! Allocate a temporary buffer for the iluk_copyin function
!
call trw%allocate(izero,izero,ione)
if (info == psb_success_) call psb_ensure_size(m+1,lirp,info)
if (info == psb_success_) call psb_ensure_size(m+1,uirp,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_sp_all')
goto 9999
end if
l1=0
l2=0
lirp(1) = 1
uirp(1) = 1
!
! Allocate memory to hold the entries of a row and the corresponding
! fill levels
!
allocate(uplevs(size(uval)),rowlevs(m),row(m),stat=info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
uplevs(:) = m+1
row(:) = czero
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) = czero
if (i<=ma) then
!
! Copy into trw the i-th local row of the matrix, stored in a
!
call iluk_copyin(i,ma,a,ione,m,row,rowlevs,heap,ktrw,trw,info,shft)
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,ione,m,row,rowlevs,heap,ktrw,trw,info,shft)
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.
!
if (info == psb_success_) call iluk_fact(fill_in,i,row,rowlevs,heap,&
& d,uja,uirp,uval,uplevs,nidx,idxs,info)
!
! Copy the row into lval/d(i)/uval
!
if (info == psb_success_) call iluk_copyout(fill_in,ialg,i,m,row,rowlevs,nidx,idxs,&
& l1,l2,lja,lirp,lval,d,uja,uirp,uval,uplevs,info)
if (info /= psb_success_) then
info=psb_err_internal_error_
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(uplevs,rowlevs,row,stat=info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='Deallocate')
goto 9999
end if
if (info == psb_success_) call trw%free()
if (info /= psb_success_) then
info=psb_err_from_subroutine_
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 call psb_error_handler(err_act)
return
end subroutine psb_ciluk_factint
!
! Subroutine: iluk_copyin
! Version: complex
! Note: internal subroutine of psb_ciluk_fact
!
! 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 psb_iluk_factint).
! 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 psb_ciluk_factint 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_cspmat_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(psb_spk_), dimension(:), input/output.
! In input it is the null vector (see psb_iluk_factint 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_i_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_cspmat_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,info,shft)
use psb_base_mod
implicit none
! Arguments
type(psb_cspmat_type), intent(in) :: a
type(psb_c_coo_sparse_mat), intent(inout) :: trw
integer(psb_ipk_), intent(in) :: i,m,jmin,jmax
integer(psb_ipk_), intent(inout) :: ktrw,info
integer(psb_ipk_), intent(inout) :: rowlevs(:)
complex(psb_spk_), intent(inout) :: row(:)
type(psb_i_heap), intent(inout) :: heap
complex(psb_spk_), intent(in) :: shft
! Local variables
integer(psb_ipk_) :: k,j,irb,err_act,nz
integer(psb_ipk_), parameter :: nrb=40
character(len=20), parameter :: name='iluk_copyin'
character(len=20) :: ch_err
info=psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
call heap%init(info)
select type (aa=> a%a)
type is (psb_c_csr_sparse_mat)
!
! Take a fast shortcut if the matrix is stored in CSR format
!
do j = aa%irp(i), aa%irp(i+1) - 1
k = aa%ja(j)
if ((jmin<=k).and.(k<=jmax)) then
row(k) = aa%val(j)
if (k==i) row(k) = row(k) + shft
rowlevs(k) = 0
call heap%insert(k,info)
end if
end do
class default
!
! 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 aa%csget(i,i+irb-1,trw,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
ch_err='psb_sp_getblk'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
ktrw=1
end if
nz = trw%get_nzeros()
do
if (ktrw > nz) exit
if (trw%ia(ktrw) > i) exit
k = trw%ja(ktrw)
if ((jmin<=k).and.(k<=jmax)) then
row(k) = trw%val(ktrw)
if (k==i) row(k) = row(k) + shft
rowlevs(k) = 0
call heap%insert(k,info)
end if
ktrw = ktrw + 1
enddo
end select
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
end subroutine iluk_copyin
!
! Subroutine: iluk_fact
! Version: complex
! Note: internal subroutine of psb_ciluk_fact
!
! This routine does an elimination step of the ILU(k) factorization on a
! single matrix row (see the calling routine psb_iluk_factint).
!
! This step is also the base for a MILU(k) elimination step on the row (see
! iluk_copyout). This routine is used by psb_ciluk_factint 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.
! row - complex(psb_spk_), 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_i_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(psb_spk_), input.
! The inverse of the diagonal entries of the part of the U factor
! above the current row (see iluk_copyout).
! uja - integer, dimension(:), input.
! The column indices of the nonzero entries of the part of the U
! factor above the current row, stored in uval row by row (see
! iluk_copyout, called by psb_ciluk_factint), according to the CSR
! storage format.
! uirp - integer, dimension(:), input.
! The indices identifying the first nonzero entry of each row of
! the U factor above the current row, stored in uval row by row
! (see iluk_copyout, called by psb_ciluk_factint), according to
! the CSR storage format.
! uval - complex(psb_spk_), 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,row,rowlevs,heap,d,&
& uja,uirp,uval,uplevs,nidx,idxs,info)
use psb_base_mod
implicit none
! Arguments
type(psb_i_heap), intent(inout) :: heap
integer(psb_ipk_), intent(in) :: i, fill_in
integer(psb_ipk_), intent(inout) :: nidx,info
integer(psb_ipk_), intent(inout) :: rowlevs(:)
integer(psb_ipk_), allocatable, intent(inout) :: idxs(:)
integer(psb_ipk_), intent(inout) :: uja(:),uirp(:),uplevs(:)
complex(psb_spk_), intent(inout) :: row(:), uval(:),d(:)
! Local variables
integer(psb_ipk_) :: k,j,lrwk,jj,lastk, iret
complex(psb_spk_) :: rwk
info = psb_success_
if (.not.allocated(idxs)) then
allocate(idxs(200),stat=info)
if (info /= psb_success_) return
endif
nidx = 0
lastk = -1
!
! Do while there are indices to be processed
!
do
! Beware: (iret < 0) means that the heap is empty, not an error.
call heap%get_first(k,iret)
if (iret < 0) return
!
! 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)
if (info /= psb_success_) return
end if
idxs(nidx) = k
if ((row(k) /= czero).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=uirp(k),uirp(k+1)-1
j = uja(jj)
if (j<=k) then
info = -i
return
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 heap%insert(j,info)
if (info /= psb_success_) return
rowlevs(j) = abs(rowlevs(j))
end if
!
! Update row(j) and the corresponding fill level
!
row(j) = row(j) - rwk * uval(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 psb_ciluk_fact
!
! This routine copies a matrix row, computed by iluk_fact by applying an
! elimination step of the ILU(k) factorization, into the arrays lval, uval,
! d, corresponding to the L factor, the U factor and the diagonal of U,
! respectively.
!
! Note that
! - the part of the row stored into uval 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 == psb_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 lval and uval according to the CSR format;
! - the arrays row and rowlevs are re-initialized for future use in psb_iluk_fact
! (see also iluk_copyin and iluk_fact).
!
! This routine is used by psb_ciluk_factint 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 (= psb_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(psb_spk_), 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 psb_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 psb_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 lval.
! l2 - integer, input/output.
! Pointer to the last occupied entry of uval.
! lja - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the L factor,
! copied in lval row by row (see psb_ciluk_factint), according
! to the CSR storage format.
! lirp - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the L factor, copied in lval row by row (see
! psb_ciluk_factint), according to the CSR storage format.
! lval - complex(psb_spk_), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! L factor are copied.
! d - complex(psb_spk_), 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).
! uja - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the U factor
! copied in uval row by row (see psb_ciluk_factint), according
! to the CSR storage format.
! uirp - integer, dimension(:), input/output.
! The indices identifying the first nonzero entry of each row
! of the U factor copied in uval row by row (see
! psb_zilu_fctint), according to the CSR storage format.
! uval - complex(psb_spk_), 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,lja,lirp,lval,d,uja,uirp,uval,uplevs,info)
use psb_base_mod
implicit none
! Arguments
integer(psb_ipk_), intent(in) :: fill_in, ialg, i, m, nidx
integer(psb_ipk_), intent(inout) :: l1, l2, info
integer(psb_ipk_), intent(inout) :: rowlevs(:), idxs(:)
integer(psb_ipk_), allocatable, intent(inout) :: uja(:), uirp(:), lja(:), lirp(:),uplevs(:)
complex(psb_spk_), allocatable, intent(inout) :: uval(:), lval(:)
complex(psb_spk_), intent(inout) :: row(:), d(:)
! Local variables
integer(psb_ipk_) :: j,isz,err_act,int_err(5),idxp
character(len=20), parameter :: name='psb_ciluk_factint'
character(len=20) :: ch_err
info = psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
d(i) = czero
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(lval) < l1) then
!
! Figure out a good reallocation size!
!
isz = (max((l1/i)*m,int(1.2*l1),l1+100))
call psb_realloc(isz,lval,info)
if (info == psb_success_) call psb_realloc(isz,lja,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
end if
lja(l1) = j
lval(l1) = row(j)
else if (ialg == psb_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) = czero
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) = czero
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(uval) < l2) then
!
! Figure out a good reallocation size!
!
isz = max((l2/i)*m,int(1.2*l2),l2+100)
call psb_realloc(isz,uval,info)
if (info == psb_success_) call psb_realloc(isz,uja,info)
if (info == psb_success_) call psb_realloc(isz,uplevs,info,pad=(m+1))
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
end if
uja(l2) = j
uval(l2) = row(j)
uplevs(l2) = rowlevs(j)
else if (ialg == psb_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) = czero
rowlevs(j) = -(m+1)
end if
end do
!
! Store the pointers to the first non occupied entry of in
! lval and uval
!
lirp(i+1) = l1 + 1
uirp(i+1) = l2 + 1
!
! Check the pivot size
!
if (abs(d(i)) < s_epstol) then
!
! Too small pivot: unstable factorization
!
info = psb_err_pivot_too_small_
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) = cone/d(i)
end if
!
! Scale the upper part
!
do j=uirp(i), uirp(i+1)-1
uval(j) = d(i)*uval(j)
end do
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
end subroutine iluk_copyout
end subroutine psb_ciluk_fact