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968 lines
37 KiB
Fortran
968 lines
37 KiB
Fortran
!!$
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!!$
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!!$ MLD2P4
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS v.2.0)
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!!$
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!!$ (C) Copyright 2007 Alfredo Buttari University of Rome Tor Vergata
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!!$ Pasqua D'Ambra ICAR-CNR, Naples
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!!$ Daniela di Serafino Second University of Naples
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the MLD2P4 group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! File: mld_ziluk_fact.f90
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!
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! Subroutine: mld_ziluk_fact
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! Version: complex
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! Contains: mld_ziluk_factint, iluk_copyin, iluk_fact, iluk_copyout
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!
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! This routine computes either the ILU(k) or the MILU(k) factorization of the
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! local part of the matrix stored into a. These factorizations are used to
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! build the 'base preconditioner' (block-Jacobi preconditioner/solver, Additive
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! Schwarz preconditioner) corresponding to a certain level of a multilevel
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! preconditioner.
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!
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! Details on the above factorizations can be found in
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! Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition,
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! SIAM, 2003, Chapter 10.
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!
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! The local matrix to be factorized is stored into a and blck, as specified in
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! the description of the arguments below. The storage format for both the L and
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! U factors is CSR. The diagonal of the U factor is stored separately (actually,
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! the inverse of the diagonal entries is stored; this is then managed in the solve
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! stage associated to the ILU(k)/MILU(k) factorization).
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!
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!
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! Arguments:
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! fill_in - integer, input.
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! The fill-in level k in ILU(k)/MILU(k).
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! ialg - integer, input.
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! The type of incomplete factorization to be performed.
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! The MILU(k) factorization is computed if ialg = 2 (= mld_milu_n_);
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! the ILU(k) factorization otherwise.
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! a - type(psb_zspmat_type), input.
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! The sparse matrix structure containing the local matrix to be
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! factorized. Note that if the 'base' Additive Schwarz preconditioner
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! has overlap greater than 0 and the matrix has not been reordered
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! (see mld_bjac_bld), then a contains only the 'original' local part
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! of the matrix to be factorized, i.e. the rows of the matrix held
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! by the calling process according to the initial data distribution.
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! l - type(psb_zspmat_type), input/output.
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! The L factor in the incomplete factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! u - type(psb_zspmat_type), input/output.
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! The U factor (except its diagonal) in the incomplete factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! d - complex(kind(1.d0)), dimension(:), input/output.
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! The inverse of the diagonal entries of the U factor in the incomplete
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! factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! info - integer, output.
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! Error code.
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! blck - type(psb_zspmat_type), input, optional, target.
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! The sparse matrix structure containing the remote rows of the
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! matrix to be factorized, that have been retrieved by mld_asmat_bld
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! to build an Additive Schwarz base preconditioner with overlap
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! greater than 0. If the overlap is 0 or the matrix has been reordered
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! (see mld_bjac_bld), then blck does not contain any row.
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!
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subroutine mld_ziluk_fact(fill_in,ialg,a,l,u,d,info,blck)
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use psb_base_mod
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use mld_prec_mod, mld_protect_name => mld_ziluk_fact
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implicit none
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! Arguments
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integer, intent(in) :: fill_in, ialg
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integer, intent(out) :: info
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type(psb_zspmat_type),intent(in) :: a
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type(psb_zspmat_type),intent(inout) :: l,u
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type(psb_zspmat_type),intent(in), optional, target :: blck
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complex(kind(1.d0)), intent(inout) :: d(:)
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! Local Variables
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integer :: l1, l2, m, err_act
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type(psb_zspmat_type), pointer :: blck_
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character(len=20) :: name, ch_err
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name='mld_ziluk_fact'
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info = 0
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call psb_erractionsave(err_act)
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!
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! Point to / allocate memory for the incomplete factorization
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!
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if (present(blck)) then
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blck_ => blck
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else
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allocate(blck_,stat=info)
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if (info /= 0) then
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call psb_errpush(4010,name,a_err='Allocate')
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goto 9999
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end if
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call psb_sp_all(0,0,blck_,1,info)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_all'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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endif
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!
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! Compute the ILU(k) or the MILU(k) factorization, depending on ialg
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!
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call mld_ziluk_factint(fill_in,ialg,m,a,blck_,&
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& d,l%aspk,l%ia1,l%ia2,u%aspk,u%ia1,u%ia2,l1,l2,info)
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if (info /= 0) then
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info=4010
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ch_err='mld_ziluk_factint'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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!
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! Store information on the L and U sparse matrices
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!
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l%infoa(1) = l1
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l%fida = 'CSR'
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l%descra = 'TLU'
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u%infoa(1) = l2
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u%fida = 'CSR'
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u%descra = 'TUU'
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l%m = m
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l%k = m
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u%m = m
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u%k = m
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!
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! Nullify the pointer / deallocate the memory
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!
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if (present(blck)) then
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blck_ => null()
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else
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call psb_sp_free(blck_,info)
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if (info /= 0) then
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info=4010
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ch_err='psb_sp_free'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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deallocate(blck_)
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endif
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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contains
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!
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! Subroutine: mld_ziluk_factint
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! Version: complex
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! Note: internal subroutine of mld_ziluk_fact
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!
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! 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).
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!
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!
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! Arguments:
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! fill_in - integer, input.
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|
! The fill-in level k in ILU(k)/MILU(k).
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|
! ialg - integer, input.
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|
! The type of incomplete factorization to be performed.
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|
! The MILU(k) factorization is computed if ialg = 2 (= mld_milu_n_);
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! the ILU(k) factorization otherwise.
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! m - integer, output.
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! The total number of rows of the local matrix to be factorized,
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! i.e. ma+mb.
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! a - type(psb_zspmat_type), input.
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! The sparse matrix structure containing the local matrix to be
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|
! 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
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|
! of the matrix to be factorized, i.e. the rows of the matrix held
|
|
! by the calling process according to the initial data distribution.
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|
! b - type(psb_zspmat_type), input.
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|
! 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.
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|
! d - complex(kind(1.d0)), dimension(:), output.
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|
! The inverse of the diagonal entries of the U factor in the incomplete
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! factorization.
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! laspk - complex(kind(1.d0)), dimension(:), input/output.
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! The L factor in the incomplete factorization.
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|
! lia1 - integer, dimension(:), input/output.
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! The column indices of the nonzero entries of the L factor,
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|
! according to the CSR storage format.
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|
! lia2 - integer, dimension(:), input/output.
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|
! The indices identifying the first nonzero entry of each row
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|
! of the L factor in laspk, according to the CSR storage format.
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|
! uaspk - complex(kind(1.d0)), dimension(:), input/output.
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|
! The U factor in the incomplete factorization.
|
|
! The entries of U are stored according to the CSR format.
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|
! 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
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|
! of the U factor in uaspk, according to the CSR storage format.
|
|
! l1 - integer, output
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|
! The number of nonzero entries in laspk.
|
|
! l2 - integer, output
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|
! The number of nonzero entries in uaspk.
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! info - integer, output.
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|
! Error code.
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!
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subroutine mld_ziluk_factint(fill_in,ialg,m,a,b,&
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& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
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|
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|
use psb_base_mod
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
integer, intent(in) :: fill_in, ialg
|
|
type(psb_zspmat_type), intent(in) :: a,b
|
|
integer, intent(inout) :: m,l1,l2,info
|
|
integer, allocatable, intent(inout) :: lia1(:),lia2(:),uia1(:),uia2(:)
|
|
complex(kind(1.d0)), allocatable, intent(inout) :: laspk(:),uaspk(:)
|
|
complex(kind(1.d0)), intent(inout) :: d(:)
|
|
|
|
! Local variables
|
|
integer :: ma,mb,i, ktrw,err_act,nidx
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|
integer, allocatable :: uplevs(:), rowlevs(:),idxs(:)
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|
complex(kind(1.d0)), allocatable :: row(:)
|
|
type(psb_int_heap) :: heap
|
|
logical,parameter :: debug=.false.
|
|
type(psb_zspmat_type) :: trw
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|
character(len=20), parameter :: name='mld_ziluk_factint'
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|
character(len=20) :: ch_err
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|
|
|
if (psb_get_errstatus() /= 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=(/2,ialg,0,0,0/))
|
|
goto 9999
|
|
end select
|
|
if (fill_in < 0) then
|
|
info=35
|
|
call psb_errpush(info,name,i_err=(/1,fill_in,0,0,0/))
|
|
goto 9999
|
|
end if
|
|
|
|
ma = a%m
|
|
mb = b%m
|
|
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,info)
|
|
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,info)
|
|
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 == 0) call iluk_fact(fill_in,i,row,rowlevs,heap,&
|
|
& d,uia1,uia2,uaspk,uplevs,nidx,idxs,info)
|
|
!
|
|
! Copy the row into laspk/d(i)/uaspk
|
|
!
|
|
if (info == 0) call iluk_copyout(fill_in,ialg,i,m,row,rowlevs,nidx,idxs,&
|
|
& l1,l2,lia1,lia2,laspk,d,uia1,uia2,uaspk,uplevs,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(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_factint
|
|
|
|
!
|
|
! Subroutine: iluk_copyin
|
|
! Version: complex
|
|
! Note: internal subroutine of mld_ziluk_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 mld_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 mld_ziluk_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_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_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_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,info)
|
|
|
|
use psb_base_mod
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_zspmat_type), intent(in) :: a
|
|
type(psb_zspmat_type), intent(inout) :: trw
|
|
integer, intent(in) :: i,m,jmin,jmax
|
|
integer, intent(inout) :: ktrw,info
|
|
integer, intent(inout) :: rowlevs(:)
|
|
complex(kind(1.d0)), intent(inout) :: row(:)
|
|
type(psb_int_heap), intent(inout) :: heap
|
|
|
|
! Local variables
|
|
integer :: k,j,irb,err_act
|
|
integer, parameter :: nrb=16
|
|
character(len=20), parameter :: name='iluk_copyin'
|
|
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_fact
|
|
!
|
|
! This routine does an elimination step of the ILU(k) factorization on a
|
|
! single matrix row (see the calling routine mld_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 mld_ziluk_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(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_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 iluk_copyout, called by mld_ziluk_factint), 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,row,rowlevs,heap,d,uia1,uia2,uaspk,uplevs,nidx,idxs,info)
|
|
|
|
use psb_base_mod
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_int_heap), intent(inout) :: heap
|
|
integer, intent(in) :: i, fill_in
|
|
integer, intent(inout) :: nidx,info
|
|
integer, intent(inout) :: rowlevs(:)
|
|
integer, allocatable, intent(inout) :: idxs(:)
|
|
integer, intent(inout) :: uia1(:),uia2(:),uplevs(:)
|
|
complex(kind(1.d0)), intent(inout) :: row(:), uaspk(:),d(:)
|
|
|
|
! Local variables
|
|
integer :: k,j,lrwk,jj,lastk, iret
|
|
complex(kind(1.d0)) :: rwk
|
|
|
|
info = 0
|
|
if (.not.allocated(idxs)) then
|
|
allocate(idxs(200),stat=info)
|
|
if (info /= 0) 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 psb_heap_get_first(k,heap,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 /= 0) return
|
|
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
|
|
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 psb_insert_heap(j,heap,info)
|
|
if (info /= 0) return
|
|
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_fact
|
|
!
|
|
! 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_fact
|
|
! (see also iluk_copyin and iluk_fact).
|
|
!
|
|
! This routine is used by mld_ziluk_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 (= 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_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_ziluk_factint), 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_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(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,info)
|
|
|
|
use psb_base_mod
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
integer, intent(in) :: fill_in, ialg, i, m, nidx
|
|
integer, intent(inout) :: l1, l2, info
|
|
integer, intent(inout) :: rowlevs(:), idxs(:)
|
|
integer, allocatable, intent(inout) :: uia1(:), uia2(:), lia1(:), lia2(:),uplevs(:)
|
|
complex(kind(1.d0)), allocatable, intent(inout) :: uaspk(:), laspk(:)
|
|
complex(kind(1.d0)), intent(inout) :: row(:), d(:)
|
|
|
|
! Local variables
|
|
integer :: j,isz,err_act,int_err(5),idxp
|
|
character(len=20), parameter :: name='mld_ziluk_factint'
|
|
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_fact
|