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amg4psblas/mlprec/mld_dilu0_fact.f90

649 lines
23 KiB
Fortran

!!$
!!$
!!$ 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
!!$ 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: mld_dilu0_fact.f90
!
! Subroutine: mld_dilu0_fact
! Version: real
! Contains: mld_dilu0_factint, ilu_copyin
!
! This routine computes either the ILU(0) or the MILU(0) 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 given 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(0)/MILU(0) factorization).
!
! The routine copies and factors "on the fly" from a and blck into l (L factor),
! u (U factor, except its diagonal) and d (diagonal of U).
!
! This implementation of ILU(0)/MILU(0) is faster than the implementation in
! mld_diluk_fct (the latter routine performs the more general ILU(k)/MILU(k)).
!
!
! Arguments:
! ialg - integer, input.
! The type of incomplete factorization to be performed.
! The MILU(0) factorization is computed if ialg = 2 (= mld_milu_n_);
! the ILU(0) factorization otherwise.
! a - type(psb_dspmat_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_as_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_dspmat_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_dspmat_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 - real(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_dspmat_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 is empty.
!
subroutine mld_dilu0_fact(ialg,a,l,u,d,info,blck)
use psb_base_mod
use mld_inner_mod, mld_protect_name => mld_dilu0_fact
implicit none
! Arguments
integer, intent(in) :: ialg
type(psb_dspmat_type),intent(in) :: a
type(psb_dspmat_type),intent(inout) :: l,u
real(psb_dpk_), intent(inout) :: d(:)
integer, intent(out) :: info
type(psb_dspmat_type),intent(in), optional, target :: blck
! Local variables
integer :: l1, l2,m,err_act
type(psb_dspmat_type), pointer :: blck_
character(len=20) :: name, ch_err
name='mld_dilu0_fact'
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_nullify_sp(blck_) ! Probably pointless.
call psb_sp_all(0,0,blck_,1,info)
if(info.ne.0) then
info=4010
ch_err='psb_sp_all'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
blck_%m=0
endif
!
! Compute the ILU(0) or the MILU(0) factorization, depending on ialg
!
call mld_dilu0_factint(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.ne.0) then
info=4010
ch_err='mld_dilu0_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 pointer / deallocate memory
!
if (present(blck)) then
blck_ => null()
else
call psb_sp_free(blck_,info)
if(info.ne.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_dilu0_factint
! Version: real
! Note: internal subroutine of mld_dilu0_fact.
!
! This routine computes either the ILU(0) or the MILU(0) 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 given 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(0)/MILU(0) factorization).
!
! The routine copies and factors "on the fly" from the sparse matrix structures a
! and b into the arrays laspk, uaspk, d (L, U without its diagonal, diagonal of U).
!
!
! Arguments:
! ialg - integer, input.
! The type of incomplete factorization to be performed.
! The ILU(0) factorization is computed if ialg = 1 (= mld_ilu_n_),
! the MILU(0) one if ialg = 2 (= mld_milu_n_); other values
! are not allowed.
! 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_dspmat_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.
! mb - integer, input.
! The number of rows of the local submatrix stored into b.
! b - type(psb_dspmat_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 - real(psb_dpk_), dimension(:), output.
! The inverse of the diagonal entries of the U factor in the
! incomplete factorization.
! laspk - real(psb_dpk_), dimension(:), input/output.
! The entries of U are stored according to the CSR format.
! 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 - real(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_dilu0_factint(ialg,m,ma,a,mb,b,&
& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
implicit none
! Arguments
integer, intent(in) :: ialg
type(psb_dspmat_type),intent(in) :: a,b
integer,intent(inout) :: m,l1,l2,info
integer, intent(in) :: ma,mb
integer, dimension(:), intent(inout) :: lia1,lia2,uia1,uia2
real(psb_dpk_), dimension(:),intent(inout) :: laspk,uaspk,d
! Local variables
integer :: i,j,k,l,low1,low2,kk,jj,ll, ktrw,err_act
real(psb_dpk_) :: dia,temp
integer, parameter :: nrb=16
type(psb_dspmat_type) :: trw
integer :: int_err(5)
character(len=20) :: name, ch_err
name='mld_dilu0_factint'
if(psb_get_errstatus().ne.0) return
info=0
call psb_erractionsave(err_act)
select case(ialg)
case(mld_ilu_n_,mld_milu_n_)
! Ok
case default
info=35
call psb_errpush(info,name,i_err=(/1,ialg,0,0,0/))
goto 9999
end select
call psb_nullify_sp(trw)
trw%m=0
trw%k=0
call psb_sp_all(trw,1,info)
if(info.ne.0) then
info=4010
ch_err='psb_sp_all'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
lia2(1) = 1
uia2(1) = 1
l1 = 0
l2 = 0
m = ma+mb
!
! Cycle over the matrix rows
!
do i = 1, m
d(i) = dzero
if (i <= ma) then
!
! Copy the i-th local row of the matrix, stored in a,
! into laspk/d(i)/uaspk
!
call ilu_copyin(i,ma,a,i,1,m,l1,lia1,laspk,&
& d(i),l2,uia1,uaspk,ktrw,trw)
else
!
! Copy the i-th local row of the matrix, stored in b
! (as (i-ma)-th row), into laspk/d(i)/uaspk
!
call ilu_copyin(i-ma,mb,b,i,1,m,l1,lia1,laspk,&
& d(i),l2,uia1,uaspk,ktrw,trw)
endif
lia2(i+1) = l1 + 1
uia2(i+1) = l2 + 1
dia = d(i)
do kk = lia2(i), lia2(i+1) - 1
!
! Compute entry l(i,k) (lower factor L) of the incomplete
! factorization
!
temp = laspk(kk)
k = lia1(kk)
laspk(kk) = temp*d(k)
!
! Update the rest of row i (lower and upper factors L and U)
! using l(i,k)
!
low1 = kk + 1
low2 = uia2(i)
!
updateloop: do jj = uia2(k), uia2(k+1) - 1
!
j = uia1(jj)
!
if (j < i) then
!
! search l(i,*) (i-th row of L) for a matching index j
!
do ll = low1, lia2(i+1) - 1
l = lia1(ll)
if (l > j) then
low1 = ll
exit
else if (l == j) then
laspk(ll) = laspk(ll) - temp*uaspk(jj)
low1 = ll + 1
cycle updateloop
end if
enddo
else if (j == i) then
!
! j=i: update the diagonal
!
dia = dia - temp*uaspk(jj)
cycle updateloop
!
else if (j > i) then
!
! search u(i,*) (i-th row of U) for a matching index j
!
do ll = low2, uia2(i+1) - 1
l = uia1(ll)
if (l > j) then
low2 = ll
exit
else if (l == j) then
uaspk(ll) = uaspk(ll) - temp*uaspk(jj)
low2 = ll + 1
cycle updateloop
end if
enddo
end if
!
! If we get here we missed the cycle updateloop, which means
! that this entry does not match; thus we accumulate on the
! diagonal for MILU(0).
!
if (ialg == mld_milu_n_) then
dia = dia - temp*uaspk(jj)
end if
enddo updateloop
enddo
!
! Check the pivot size
!
if (abs(dia) < epstol) then
!
! Too small pivot: unstable factorization
!
info = 2
int_err(1) = i
write(ch_err,'(g20.10)') abs(dia)
call psb_errpush(info,name,i_err=int_err,a_err=ch_err)
goto 9999
else
!
! Compute 1/pivot
!
dia = done/dia
end if
d(i) = dia
!
! Scale row i of upper triangle
!
do kk = uia2(i), uia2(i+1) - 1
uaspk(kk) = uaspk(kk)*dia
enddo
enddo
call psb_sp_free(trw,info)
if(info.ne.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_dilu0_factint
!
! Subroutine: ilu_copyin
! Version: real
! Note: internal subroutine of mld_dilu0_fact
!
! This routine copies a row of a sparse matrix A, stored in the psb_dspmat_type
! data structure a, into the arrays laspk and uaspk and into the scalar variable
! dia, corresponding to the lower and upper triangles of A and to the diagonal
! entry of the row, respectively. The entries in laspk and uaspk are stored
! according to the CSR format; the corresponding column indices are stored in
! the arrays lia1 and uia1.
!
! 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 into laspk, dia, uaspk row by row, through successive calls to
! ilu_copyin.
!
! The routine is used by mld_dilu0_factint in the computation of the ILU(0)/MILU(0)
! factorization of a local sparse matrix.
!
! TODO: modify the routine to allow copying into output L and U that are
! already filled with indices; this would allow computing an ILU(k) pattern,
! then use the ILU(0) internal for subsequent calls with the same pattern.
!
! 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_dspmat_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.
! Minimum valid column index.
! jmax - integer, input.
! Maximum valid column index.
! The output matrix will contain a clipped copy taken from
! a(1:m,jmin:jmax).
! l1 - integer, input/output.
! Pointer to the last occupied entry of laspk.
! lia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the lower triangle
! copied in laspk row by row (see mld_dilu0_factint), according
! to the CSR storage format.
! laspk - real(psb_dpk_), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! lower triangle are copied.
! dia - real(psb_dpk_), output.
! The diagonal entry of the copied row.
! l2 - integer, input/output.
! Pointer to the last occupied entry of uaspk.
! uia1 - integer, dimension(:), input/output.
! The column indices of the nonzero entries of the upper triangle
! copied in uaspk row by row (see mld_dilu0_factint), according
! to the CSR storage format.
! uaspk - real(psb_dpk_), dimension(:), input/output.
! The array where the entries of the row corresponding to the
! upper triangle are copied.
! 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 ilu_copyin(i,m,a,jd,jmin,jmax,l1,lia1,laspk,&
& dia,l2,uia1,uaspk,ktrw,trw)
use psb_base_mod
implicit none
! Arguments
type(psb_dspmat_type), intent(in) :: a
type(psb_dspmat_type), intent(inout) :: trw
integer, intent(in) :: i,m,jd,jmin,jmax
integer, intent(inout) :: ktrw,l1,l2
integer, intent(inout) :: lia1(:), uia1(:)
real(psb_dpk_), intent(inout) :: laspk(:), uaspk(:), dia
! Local variables
integer :: k,j,info,irb
integer, parameter :: nrb=16
character(len=20), parameter :: name='ilu_copyin'
character(len=20) :: ch_err
if (psb_get_errstatus() /= 0) return
info=0
call psb_erractionsave(err_act)
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)
! write(0,*)'KKKKK',k
if ((k < jd).and.(k >= jmin)) then
l1 = l1 + 1
laspk(l1) = a%aspk(j)
lia1(l1) = k
else if (k == jd) then
dia = a%aspk(j)
else if ((k > jd).and.(k <= jmax)) then
l2 = l2 + 1
uaspk(l2) = a%aspk(j)
uia1(l2) = k
end if
enddo
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 laspk, dia, uaspk, through
! successive calls to ilu_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.ne.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 ((k < jd).and.(k >= jmin)) then
l1 = l1 + 1
laspk(l1) = trw%aspk(ktrw)
lia1(l1) = k
else if (k == jd) then
dia = trw%aspk(ktrw)
else if ((k > jd).and.(k <= jmax)) then
l2 = l2 + 1
uaspk(l2) = trw%aspk(ktrw)
uia1(l2) = k
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 ilu_copyin
end subroutine mld_dilu0_fact