Integration of psb_ilu & friends
Salvatore Filippone
4 years ago
parent
68a4ee9cd4
commit
90e1f1cfe6
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!
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!
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! MLD2P4 version 2.2
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! MultiLevel Domain Decomposition Parallel Preconditioners Package
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! based on PSBLAS (Parallel Sparse BLAS version 3.5)
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!
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! (C) Copyright 2008-2018
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!
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! Salvatore Filippone
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! Pasqua D'Ambra
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! Daniela di Serafino
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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_cilu0_fact.f90
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!
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! Subroutine: mld_cilu0_fact
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! Version: complex
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! Contains: mld_cilu0_factint, ilu_copyin
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!
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! This routine computes either the ILU(0) or the MILU(0) factorization of
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! the diagonal blocks of a distributed matrix. These factorizations are used
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! to build the 'base preconditioner' (block-Jacobi preconditioner/solver,
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! Additive Schwarz preconditioner) corresponding to a given level of a
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! multilevel 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 is stored into a and blck, as specified in the description
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! of the arguments below. The storage format for both the L and U factors is CSR.
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! The diagonal of the U factor is stored separately (actually, the inverse of the
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! diagonal entries is stored; this is then managed in the solve stage associated
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! to the ILU(0)/MILU(0) factorization).
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!
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! The routine copies and factors "on the fly" from a and blck into l (L factor),
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! u (U factor, except its diagonal) and d (diagonal of U).
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!
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! This implementation of ILU(0)/MILU(0) is faster than the implementation in
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! mld_ziluk_fct (the latter routine performs the more general ILU(k)/MILU(k)).
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!
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!
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! Arguments:
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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(0) factorization is computed if ialg = 2 (= mld_milu_n_);
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! the ILU(0) factorization otherwise.
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! a - type(psb_cspmat_type), input.
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! The sparse matrix structure containing the local matrix.
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! 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_as_bld), then a contains only the 'original' local part
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! of the distributed matrix, 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_cspmat_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_cspmat_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(psb_spk_), 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_cspmat_type), input, optional, target.
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! The sparse matrix structure containing the remote rows of the
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! distributed matrix, that have been retrieved by mld_as_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_fact_bld), then blck is empty.
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!
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subroutine mld_cilu0_fact(ialg,a,l,u,d,info,blck, upd)
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use psb_base_mod
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use mld_c_ilu_fact_mod, mld_protect_name => mld_cilu0_fact
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implicit none
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! Arguments
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integer(psb_ipk_), intent(in) :: ialg
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type(psb_cspmat_type),intent(in) :: a
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type(psb_cspmat_type),intent(inout) :: l,u
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complex(psb_spk_), intent(inout) :: d(:)
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integer(psb_ipk_), intent(out) :: info
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type(psb_cspmat_type),intent(in), optional, target :: blck
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character, intent(in), optional :: upd
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! Local variables
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integer(psb_ipk_) :: l1, l2, m, err_act
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type(psb_cspmat_type), pointer :: blck_
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type(psb_c_csr_sparse_mat) :: ll, uu
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character :: upd_
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character(len=20) :: name, ch_err
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name='mld_cilu0_fact'
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info = psb_success_
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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 == psb_success_) call blck_%csall(izero,izero,info,ione)
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if (info /= psb_success_) then
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info=psb_err_from_subroutine_
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ch_err='csall'
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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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if (present(upd)) then
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upd_ = psb_toupper(upd)
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else
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upd_ = 'F'
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end if
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m = a%get_nrows() + blck_%get_nrows()
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if ((m /= l%get_nrows()).or.(m /= u%get_nrows()).or.&
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& (m > size(d)) ) then
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write(0,*) 'Wrong allocation status for L,D,U? ',&
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& l%get_nrows(),size(d),u%get_nrows()
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info = -1
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return
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end if
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call l%mv_to(ll)
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call u%mv_to(uu)
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!
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! Compute the ILU(0) or the MILU(0) factorization, depending on ialg
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!
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call mld_cilu0_factint(ialg,a,blck_,&
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& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,upd_,info)
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if(info.ne.0) then
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info=psb_err_from_subroutine_
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ch_err='mld_cilu0_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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call l%mv_from(ll)
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call l%set_triangle()
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call l%set_unit()
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call l%set_lower()
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call u%mv_from(uu)
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call u%set_triangle()
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call u%set_unit()
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call u%set_upper()
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!
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! Nullify pointer / deallocate 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 blck_%free()
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if(info.ne.0) then
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info=psb_err_from_subroutine_
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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 call psb_error_handler(err_act)
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return
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contains
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!
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! Subroutine: mld_cilu0_factint
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! Version: complex
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! Note: internal subroutine of mld_cilu0_fact.
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!
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! This routine computes either the ILU(0) or the MILU(0) factorization of the
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! diagonal blocks of a distributed matrix.
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! These factorizations are used to build the 'base preconditioner'
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! (block-Jacobi preconditioner/solver, Additive Schwarz
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! preconditioner) corresponding to a given level of a multilevel preconditioner.
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!
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! The local matrix is stored into a and b, as specified in the
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! description of the arguments below. The storage format for both the L and U
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! 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
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! solve stage associated to the ILU(0)/MILU(0) factorization).
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!
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! The routine copies and factors "on the fly" from the sparse matrix structures a
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! and b into the arrays lval, uval, d (L, U without its diagonal, diagonal of U).
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!
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!
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! Arguments:
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! ialg - integer, input.
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! The type of incomplete factorization to be performed.
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! The ILU(0) factorization is computed if ialg = 1 (= mld_ilu_n_),
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! the MILU(0) one if ialg = 2 (= mld_milu_n_); other values
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! are not allowed.
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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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! ma - integer, input
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! The number of rows of the local submatrix stored into a.
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! a - type(psb_cspmat_type), input.
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! The sparse matrix structure containing the local matrix.
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! 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_fact_bld), then a contains only the 'original' local part
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! of the distributed matrix, 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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! mb - integer, input.
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! The number of rows of the local submatrix stored into b.
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! b - type(psb_cspmat_type), input.
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! The sparse matrix structure containing the remote rows of the
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! distributed matrix, that have been retrieved by mld_as_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
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! reordered (see mld_fact_bld), then b does not contain any row.
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! d - complex(psb_spk_), dimension(:), output.
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! The inverse of the diagonal entries of the U factor in the
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! incomplete factorization.
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! lval - complex(psb_spk_), dimension(:), input/output.
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! The entries of U are stored according to the CSR format.
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! The L factor in the incomplete factorization.
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! lja - 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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! lirp - 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 lval, according to the CSR storage format.
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! uval - complex(psb_spk_), dimension(:), input/output.
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! The U factor in the incomplete factorization.
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! The entries of U are stored according to the CSR format.
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! uja - integer, dimension(:), input/output.
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! The column indices of the nonzero entries of the U factor,
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! according to the CSR storage format.
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! uirp - integer, dimension(:), input/output.
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! The indices identifying the first nonzero entry of each row
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! of the U factor in uval, according to the CSR storage format.
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! l1 - integer, output.
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! The number of nonzero entries in lval.
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! l2 - integer, output.
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! The number of nonzero entries in uval.
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! info - integer, output.
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! Error code.
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!
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subroutine mld_cilu0_factint(ialg,a,b,&
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& d,lval,lja,lirp,uval,uja,uirp,l1,l2,upd,info)
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implicit none
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! Arguments
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integer(psb_ipk_), intent(in) :: ialg
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type(psb_cspmat_type),intent(in) :: a,b
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integer(psb_ipk_),intent(inout) :: l1,l2,info
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integer(psb_ipk_), intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
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complex(psb_spk_), intent(inout) :: lval(:),uval(:),d(:)
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character, intent(in) :: upd
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! Local variables
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integer(psb_ipk_) :: i,j,k,l,low1,low2,kk,jj,ll, ktrw,err_act, m
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integer(psb_ipk_) :: ma,mb
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complex(psb_spk_) :: dia,temp
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integer(psb_ipk_), parameter :: nrb=16
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type(psb_c_coo_sparse_mat) :: trw
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integer(psb_ipk_) :: int_err(5)
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character(len=20) :: name, ch_err
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name='mld_cilu0_factint'
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info=psb_success_
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call psb_erractionsave(err_act)
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if (psb_errstatus_fatal()) then
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info = psb_err_internal_error_; goto 9999
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end if
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ma = a%get_nrows()
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mb = b%get_nrows()
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select case(ialg)
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case(mld_ilu_n_,mld_milu_n_)
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! Ok
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case default
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info=psb_err_input_asize_invalid_i_
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call psb_errpush(info,name,&
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& i_err=(/ione,ialg,izero,izero,izero/))
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goto 9999
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end select
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call trw%allocate(izero,izero,ione)
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if(info /= psb_success_) then
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info=psb_err_from_subroutine_
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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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m = ma+mb
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if (psb_toupper(upd) == 'F' ) then
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lirp(1) = 1
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uirp(1) = 1
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l1 = 0
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l2 = 0
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!
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! Cycle over the matrix rows
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!
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do i = 1, m
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d(i) = czero
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if (i <= ma) then
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!
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! Copy the i-th local row of the matrix, stored in a,
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|
||||||
! into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i,ma,a,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
else
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in b
|
|
||||||
! (as (i-ma)-th row), into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i-ma,mb,b,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
endif
|
|
||||||
|
|
||||||
lirp(i+1) = l1 + 1
|
|
||||||
uirp(i+1) = l2 + 1
|
|
||||||
|
|
||||||
dia = d(i)
|
|
||||||
do kk = lirp(i), lirp(i+1) - 1
|
|
||||||
!
|
|
||||||
! Compute entry l(i,k) (lower factor L) of the incomplete
|
|
||||||
! factorization
|
|
||||||
!
|
|
||||||
temp = lval(kk)
|
|
||||||
k = lja(kk)
|
|
||||||
lval(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 = uirp(i)
|
|
||||||
!
|
|
||||||
updateloop: do jj = uirp(k), uirp(k+1) - 1
|
|
||||||
!
|
|
||||||
j = uja(jj)
|
|
||||||
!
|
|
||||||
if (j < i) then
|
|
||||||
!
|
|
||||||
! search l(i,*) (i-th row of L) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low1, lirp(i+1) - 1
|
|
||||||
l = lja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low1 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
lval(ll) = lval(ll) - temp*uval(jj)
|
|
||||||
low1 = ll + 1
|
|
||||||
cycle updateloop
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
else if (j == i) then
|
|
||||||
!
|
|
||||||
! j=i: update the diagonal
|
|
||||||
!
|
|
||||||
dia = dia - temp*uval(jj)
|
|
||||||
cycle updateloop
|
|
||||||
!
|
|
||||||
else if (j > i) then
|
|
||||||
!
|
|
||||||
! search u(i,*) (i-th row of U) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low2, uirp(i+1) - 1
|
|
||||||
l = uja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low2 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
uval(ll) = uval(ll) - temp*uval(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*uval(jj)
|
|
||||||
end if
|
|
||||||
enddo updateloop
|
|
||||||
enddo
|
|
||||||
!
|
|
||||||
! Check the pivot size
|
|
||||||
!
|
|
||||||
if (abs(dia) < s_epstol) then
|
|
||||||
!
|
|
||||||
! Too small pivot: unstable factorization
|
|
||||||
!
|
|
||||||
info = psb_err_pivot_too_small_
|
|
||||||
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 = cone/dia
|
|
||||||
end if
|
|
||||||
d(i) = dia
|
|
||||||
!
|
|
||||||
! Scale row i of upper triangle
|
|
||||||
!
|
|
||||||
do kk = uirp(i), uirp(i+1) - 1
|
|
||||||
uval(kk) = uval(kk)*dia
|
|
||||||
enddo
|
|
||||||
enddo
|
|
||||||
else
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call trw%free()
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine mld_cilu0_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: ilu_copyin
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_cilu0_fact
|
|
||||||
!
|
|
||||||
! This routine copies a row of a sparse matrix A, stored in the psb_cspmat_type
|
|
||||||
! data structure a, into the arrays lval and uval 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 lval and uval are stored
|
|
||||||
! according to the CSR format; the corresponding column indices are stored in
|
|
||||||
! the arrays lja and uja.
|
|
||||||
!
|
|
||||||
! 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 lval, dia, uval row by row, through successive calls to
|
|
||||||
! ilu_copyin.
|
|
||||||
!
|
|
||||||
! The routine is used by mld_cilu0_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_cspmat_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 lval.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the lower triangle
|
|
||||||
! copied in lval row by row (see mld_cilu0_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
|
|
||||||
! lower triangle are copied.
|
|
||||||
! dia - complex(psb_spk_), output.
|
|
||||||
! The diagonal entry of the copied row.
|
|
||||||
! l2 - integer, input/output.
|
|
||||||
! Pointer to the last occupied entry of uval.
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the upper triangle
|
|
||||||
! copied in uval row by row (see mld_cilu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! uval - complex(psb_spk_), 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_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 ilu_copyin(i,m,a,jd,jmin,jmax,l1,lja,lval,&
|
|
||||||
& dia,l2,uja,uval,ktrw,trw,upd)
|
|
||||||
|
|
||||||
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,jd,jmin,jmax
|
|
||||||
integer(psb_ipk_), intent(inout) :: ktrw,l1,l2
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:), uja(:)
|
|
||||||
complex(psb_spk_), intent(inout) :: lval(:), uval(:), dia
|
|
||||||
character, intent(in) :: upd
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,info,irb, nz
|
|
||||||
integer(psb_ipk_), parameter :: nrb=40
|
|
||||||
character(len=20), parameter :: name='ilu_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
|
|
||||||
if (psb_toupper(upd) == 'F') then
|
|
||||||
|
|
||||||
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)
|
|
||||||
! write(0,*)'KKKKK',k
|
|
||||||
if ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = aa%val(j)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = aa%val(j)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = aa%val(j)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
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 lval, dia, uval, through
|
|
||||||
! successive calls to ilu_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='csget'
|
|
||||||
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 ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = trw%val(ktrw)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = trw%val(ktrw)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = trw%val(ktrw)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
ktrw = ktrw + 1
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end select
|
|
||||||
|
|
||||||
else
|
|
||||||
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine ilu_copyin
|
|
||||||
|
|
||||||
end subroutine mld_cilu0_fact
|
|
||||||
@ -1,969 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_ciluk_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_ciluk_fact
|
|
||||||
! Version: complex
|
|
||||||
! Contains: mld_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 (= mld_ilu_n_);
|
|
||||||
! the MILU(k) one if ialg = 2 (= mld_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 mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! l - type(psb_cspmat_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_cspmat_type), input/output.
|
|
||||||
! The U factor (except its diagonal) in the incomplete factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! d - complex(psb_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 mld_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 mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then blck does not contain any row.
|
|
||||||
!
|
|
||||||
subroutine mld_ciluk_fact(fill_in,ialg,a,l,u,d,info,blck)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_c_ilu_fact_mod, mld_protect_name => mld_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(:)
|
|
||||||
! Local Variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
|
|
||||||
type(psb_cspmat_type), pointer :: blck_
|
|
||||||
type(psb_c_csr_sparse_mat) :: ll, uu
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
|
|
||||||
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 mld_ciluk_factint(fill_in,ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,info)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_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: mld_ciluk_factint
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_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 (= mld_milu_n_);
|
|
||||||
! the ILU(k) factorization otherwise.
|
|
||||||
! m - integer, output.
|
|
||||||
! The total number of rows of the local matrix to be factorized,
|
|
||||||
! i.e. ma+mb.
|
|
||||||
! 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 mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! b - type(psb_cspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then b does not contain any row.
|
|
||||||
! d - complex(psb_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 mld_ciluk_factint(fill_in,ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,info)
|
|
||||||
|
|
||||||
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(:)
|
|
||||||
|
|
||||||
! 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='mld_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(mld_ilu_n_,mld_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)
|
|
||||||
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)
|
|
||||||
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 mld_ciluk_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: iluk_copyin
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_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 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_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 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_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)
|
|
||||||
|
|
||||||
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
|
|
||||||
|
|
||||||
! 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)
|
|
||||||
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)
|
|
||||||
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 mld_ciluk_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_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 mld_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 mld_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 mld_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 == 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 lval and uval 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_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 (= 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(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 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 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 mld_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
|
|
||||||
! mld_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 mld_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
|
|
||||||
! mld_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='mld_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 == 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) = 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 == 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) = 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 mld_ciluk_fact
|
|
||||||
File diff suppressed because it is too large
Load Diff
@ -1,666 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: 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_ziluk_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, upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_d_ilu_fact_mod, mld_protect_name => mld_dilu0_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), 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(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_dspmat_type),intent(in), optional, target :: blck
|
|
||||||
character, intent(in), optional :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
type(psb_dspmat_type), pointer :: blck_
|
|
||||||
type(psb_d_csr_sparse_mat) :: ll, uu
|
|
||||||
character :: upd_
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_dilu0_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
if (present(upd)) then
|
|
||||||
upd_ = psb_toupper(upd)
|
|
||||||
else
|
|
||||||
upd_ = 'F'
|
|
||||||
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(0) or the MILU(0) factorization, depending on ialg
|
|
||||||
!
|
|
||||||
call mld_dilu0_factint(ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,upd_,info)
|
|
||||||
if(info.ne.0) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
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
|
|
||||||
!
|
|
||||||
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()
|
|
||||||
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
|
|
||||||
deallocate(blck_)
|
|
||||||
endif
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
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 lval, uval, 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.
|
|
||||||
! lval - real(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The entries of U are stored according to the CSR format.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the L factor,
|
|
||||||
! 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 in lval, according to the CSR storage format.
|
|
||||||
! uval - real(psb_dpk_), 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 lval.
|
|
||||||
! l2 - integer, output.
|
|
||||||
! The number of nonzero entries in uval.
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
!
|
|
||||||
subroutine mld_dilu0_factint(ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,upd,info)
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: ialg
|
|
||||||
type(psb_dspmat_type),intent(in) :: a,b
|
|
||||||
integer(psb_ipk_),intent(inout) :: l1,l2,info
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: lval(:),uval(:),d(:)
|
|
||||||
character, intent(in) :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: i,j,k,l,low1,low2,kk,jj,ll, ktrw,err_act, m
|
|
||||||
integer(psb_ipk_) :: ma,mb
|
|
||||||
real(psb_dpk_) :: dia,temp
|
|
||||||
integer(psb_ipk_), parameter :: nrb=16
|
|
||||||
type(psb_d_coo_sparse_mat) :: trw
|
|
||||||
integer(psb_ipk_) :: int_err(5)
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_dilu0_factint'
|
|
||||||
info=psb_success_
|
|
||||||
call psb_erractionsave(err_act)
|
|
||||||
if (psb_errstatus_fatal()) then
|
|
||||||
info = psb_err_internal_error_; goto 9999
|
|
||||||
end if
|
|
||||||
ma = a%get_nrows()
|
|
||||||
mb = b%get_nrows()
|
|
||||||
|
|
||||||
select case(ialg)
|
|
||||||
case(mld_ilu_n_,mld_milu_n_)
|
|
||||||
! Ok
|
|
||||||
case default
|
|
||||||
info=psb_err_input_asize_invalid_i_
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione,ialg,izero,izero,izero/))
|
|
||||||
goto 9999
|
|
||||||
end select
|
|
||||||
|
|
||||||
call trw%allocate(izero,izero,ione)
|
|
||||||
if(info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='psb_sp_all'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
m = ma+mb
|
|
||||||
|
|
||||||
if (psb_toupper(upd) == 'F' ) then
|
|
||||||
lirp(1) = 1
|
|
||||||
uirp(1) = 1
|
|
||||||
l1 = 0
|
|
||||||
l2 = 0
|
|
||||||
|
|
||||||
!
|
|
||||||
! 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 lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i,ma,a,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
else
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in b
|
|
||||||
! (as (i-ma)-th row), into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i-ma,mb,b,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
endif
|
|
||||||
|
|
||||||
lirp(i+1) = l1 + 1
|
|
||||||
uirp(i+1) = l2 + 1
|
|
||||||
|
|
||||||
dia = d(i)
|
|
||||||
do kk = lirp(i), lirp(i+1) - 1
|
|
||||||
!
|
|
||||||
! Compute entry l(i,k) (lower factor L) of the incomplete
|
|
||||||
! factorization
|
|
||||||
!
|
|
||||||
temp = lval(kk)
|
|
||||||
k = lja(kk)
|
|
||||||
lval(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 = uirp(i)
|
|
||||||
!
|
|
||||||
updateloop: do jj = uirp(k), uirp(k+1) - 1
|
|
||||||
!
|
|
||||||
j = uja(jj)
|
|
||||||
!
|
|
||||||
if (j < i) then
|
|
||||||
!
|
|
||||||
! search l(i,*) (i-th row of L) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low1, lirp(i+1) - 1
|
|
||||||
l = lja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low1 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
lval(ll) = lval(ll) - temp*uval(jj)
|
|
||||||
low1 = ll + 1
|
|
||||||
cycle updateloop
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
else if (j == i) then
|
|
||||||
!
|
|
||||||
! j=i: update the diagonal
|
|
||||||
!
|
|
||||||
dia = dia - temp*uval(jj)
|
|
||||||
cycle updateloop
|
|
||||||
!
|
|
||||||
else if (j > i) then
|
|
||||||
!
|
|
||||||
! search u(i,*) (i-th row of U) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low2, uirp(i+1) - 1
|
|
||||||
l = uja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low2 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
uval(ll) = uval(ll) - temp*uval(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*uval(jj)
|
|
||||||
end if
|
|
||||||
enddo updateloop
|
|
||||||
enddo
|
|
||||||
!
|
|
||||||
! Check the pivot size
|
|
||||||
!
|
|
||||||
if (abs(dia) < d_epstol) then
|
|
||||||
!
|
|
||||||
! Too small pivot: unstable factorization
|
|
||||||
!
|
|
||||||
info = psb_err_pivot_too_small_
|
|
||||||
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 = uirp(i), uirp(i+1) - 1
|
|
||||||
uval(kk) = uval(kk)*dia
|
|
||||||
enddo
|
|
||||||
enddo
|
|
||||||
else
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call trw%free()
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
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 lval and uval 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 lval and uval are stored
|
|
||||||
! according to the CSR format; the corresponding column indices are stored in
|
|
||||||
! the arrays lja and uja.
|
|
||||||
!
|
|
||||||
! 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 lval, dia, uval 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 lval.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the lower triangle
|
|
||||||
! copied in lval row by row (see mld_dilu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! lval - 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 uval.
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the upper triangle
|
|
||||||
! copied in uval row by row (see mld_dilu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! uval - 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,lja,lval,&
|
|
||||||
& dia,l2,uja,uval,ktrw,trw,upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
type(psb_dspmat_type), intent(in) :: a
|
|
||||||
type(psb_d_coo_sparse_mat), intent(inout) :: trw
|
|
||||||
integer(psb_ipk_), intent(in) :: i,m,jd,jmin,jmax
|
|
||||||
integer(psb_ipk_), intent(inout) :: ktrw,l1,l2
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:), uja(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: lval(:), uval(:), dia
|
|
||||||
character, intent(in) :: upd
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,info,irb, nz
|
|
||||||
integer(psb_ipk_), parameter :: nrb=40
|
|
||||||
character(len=20), parameter :: name='ilu_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
|
|
||||||
if (psb_toupper(upd) == 'F') then
|
|
||||||
|
|
||||||
select type(aa => a%a)
|
|
||||||
type is (psb_d_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)
|
|
||||||
! write(0,*)'KKKKK',k
|
|
||||||
if ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = aa%val(j)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = aa%val(j)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = aa%val(j)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
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 lval, dia, uval, through
|
|
||||||
! successive calls to ilu_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='csget'
|
|
||||||
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 ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = trw%val(ktrw)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = trw%val(ktrw)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = trw%val(ktrw)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
ktrw = ktrw + 1
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end select
|
|
||||||
|
|
||||||
else
|
|
||||||
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine ilu_copyin
|
|
||||||
|
|
||||||
end subroutine mld_dilu0_fact
|
|
||||||
@ -1,969 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_diluk_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_diluk_fact
|
|
||||||
! Version: real
|
|
||||||
! Contains: mld_diluk_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 (= mld_ilu_n_);
|
|
||||||
! the MILU(k) one if ialg = 2 (= mld_milu_n_); other values are
|
|
||||||
! not allowed.
|
|
||||||
! 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.
|
|
||||||
! 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 does not contain any row.
|
|
||||||
!
|
|
||||||
subroutine mld_diluk_fact(fill_in,ialg,a,l,u,d,info,blck)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_d_ilu_fact_mod, mld_protect_name => mld_diluk_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
integer(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_dspmat_type),intent(in) :: a
|
|
||||||
type(psb_dspmat_type),intent(inout) :: l,u
|
|
||||||
type(psb_dspmat_type),intent(in), optional, target :: blck
|
|
||||||
real(psb_dpk_), intent(inout) :: d(:)
|
|
||||||
! Local Variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
|
|
||||||
type(psb_dspmat_type), pointer :: blck_
|
|
||||||
type(psb_d_csr_sparse_mat) :: ll, uu
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_diluk_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
|
|
||||||
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 mld_diluk_factint(fill_in,ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,info)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_diluk_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: mld_diluk_factint
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_diluk_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 (= mld_milu_n_);
|
|
||||||
! the ILU(k) factorization otherwise.
|
|
||||||
! m - integer, output.
|
|
||||||
! The total number of rows of the local matrix to be factorized,
|
|
||||||
! i.e. ma+mb.
|
|
||||||
! 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.
|
|
||||||
! 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 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 - real(psb_dpk_), 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 mld_diluk_factint(fill_in,ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,info)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
type(psb_dspmat_type),intent(in) :: a,b
|
|
||||||
integer(psb_ipk_),intent(inout) :: l1,l2,info
|
|
||||||
integer(psb_ipk_), allocatable, intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
|
|
||||||
real(psb_dpk_), allocatable, intent(inout) :: lval(:),uval(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: ma,mb,i, ktrw,err_act,nidx, m
|
|
||||||
integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:)
|
|
||||||
real(psb_dpk_), allocatable :: row(:)
|
|
||||||
type(psb_i_heap) :: heap
|
|
||||||
type(psb_d_coo_sparse_mat) :: trw
|
|
||||||
character(len=20), parameter :: name='mld_diluk_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(mld_ilu_n_,mld_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(:) = dzero
|
|
||||||
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) = dzero
|
|
||||||
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)
|
|
||||||
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)
|
|
||||||
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 mld_diluk_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: iluk_copyin
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_diluk_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_diluk_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_dspmat_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 - real(psb_dpk_), 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_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_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_dspmat_type), intent(in) :: a
|
|
||||||
type(psb_d_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(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: row(:)
|
|
||||||
type(psb_i_heap), intent(inout) :: heap
|
|
||||||
|
|
||||||
! 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_d_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)
|
|
||||||
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)
|
|
||||||
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: real
|
|
||||||
! Note: internal subroutine of mld_diluk_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_diluk_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 - real(psb_dpk_), dimension(:), input/output.
|
|
||||||
! In input it contains the row to which the elimination step
|
|
||||||
! has to be applied. In output it contains the row after the
|
|
||||||
! elimination step. It actually contains a full row, i.e.
|
|
||||||
! it contains also the zero entries of the row.
|
|
||||||
! 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 - real(psb_dpk_), 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 mld_diluk_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 mld_diluk_factint), according to
|
|
||||||
! the CSR storage format.
|
|
||||||
! uval - real(psb_dpk_), 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(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: row(:), uval(:),d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,lrwk,jj,lastk, iret
|
|
||||||
real(psb_dpk_) :: 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) /= dzero).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: real
|
|
||||||
! Note: internal subroutine of mld_diluk_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 == 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 lval and uval 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_diluk_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 - real(psb_dpk_), dimension(:), input/output.
|
|
||||||
! It contains, input, the row to be copied, and, in output,
|
|
||||||
! the null vector (the latter is used in the next call to
|
|
||||||
! 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 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 mld_diluk_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
|
|
||||||
! mld_diluk_factint), according to the CSR storage format.
|
|
||||||
! lval - real(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The array where the entries of the row corresponding to the
|
|
||||||
! L factor are copied.
|
|
||||||
! d - real(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The array where the inverse of the diagonal entry of the
|
|
||||||
! row is copied (only d(i) is used by the routine).
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the U factor
|
|
||||||
! copied in uval row by row (see mld_diluk_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
|
|
||||||
! mld_zilu_fctint), according to the CSR storage format.
|
|
||||||
! uval - real(psb_dpk_), 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(:)
|
|
||||||
real(psb_dpk_), allocatable, intent(inout) :: uval(:), lval(:)
|
|
||||||
real(psb_dpk_), intent(inout) :: row(:), d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: j,isz,err_act,int_err(5),idxp
|
|
||||||
character(len=20), parameter :: name='mld_diluk_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) = 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(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 == 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) = dzero
|
|
||||||
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) = dzero
|
|
||||||
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 == 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) = dzero
|
|
||||||
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)) < d_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) = done/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 mld_diluk_fact
|
|
||||||
File diff suppressed because it is too large
Load Diff
@ -1,666 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_silu0_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_silu0_fact
|
|
||||||
! Version: real
|
|
||||||
! Contains: mld_silu0_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_ziluk_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_sspmat_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_sspmat_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_sspmat_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_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 mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
! blck - type(psb_sspmat_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_silu0_fact(ialg,a,l,u,d,info,blck, upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_s_ilu_fact_mod, mld_protect_name => mld_silu0_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: ialg
|
|
||||||
type(psb_sspmat_type),intent(in) :: a
|
|
||||||
type(psb_sspmat_type),intent(inout) :: l,u
|
|
||||||
real(psb_spk_), intent(inout) :: d(:)
|
|
||||||
integer(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_sspmat_type),intent(in), optional, target :: blck
|
|
||||||
character, intent(in), optional :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
type(psb_sspmat_type), pointer :: blck_
|
|
||||||
type(psb_s_csr_sparse_mat) :: ll, uu
|
|
||||||
character :: upd_
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_silu0_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
if (present(upd)) then
|
|
||||||
upd_ = psb_toupper(upd)
|
|
||||||
else
|
|
||||||
upd_ = 'F'
|
|
||||||
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(0) or the MILU(0) factorization, depending on ialg
|
|
||||||
!
|
|
||||||
call mld_silu0_factint(ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,upd_,info)
|
|
||||||
if(info.ne.0) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_silu0_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()
|
|
||||||
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
|
|
||||||
deallocate(blck_)
|
|
||||||
endif
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
contains
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: mld_silu0_factint
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_silu0_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 lval, uval, 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_sspmat_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_sspmat_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_spk_), dimension(:), output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the
|
|
||||||
! incomplete factorization.
|
|
||||||
! lval - real(psb_spk_), dimension(:), input/output.
|
|
||||||
! The entries of U are stored according to the CSR format.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the L factor,
|
|
||||||
! 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 in lval, according to the CSR storage format.
|
|
||||||
! uval - real(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 lval.
|
|
||||||
! l2 - integer, output.
|
|
||||||
! The number of nonzero entries in uval.
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
!
|
|
||||||
subroutine mld_silu0_factint(ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,upd,info)
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: ialg
|
|
||||||
type(psb_sspmat_type),intent(in) :: a,b
|
|
||||||
integer(psb_ipk_),intent(inout) :: l1,l2,info
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
|
|
||||||
real(psb_spk_), intent(inout) :: lval(:),uval(:),d(:)
|
|
||||||
character, intent(in) :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: i,j,k,l,low1,low2,kk,jj,ll, ktrw,err_act, m
|
|
||||||
integer(psb_ipk_) :: ma,mb
|
|
||||||
real(psb_spk_) :: dia,temp
|
|
||||||
integer(psb_ipk_), parameter :: nrb=16
|
|
||||||
type(psb_s_coo_sparse_mat) :: trw
|
|
||||||
integer(psb_ipk_) :: int_err(5)
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_silu0_factint'
|
|
||||||
info=psb_success_
|
|
||||||
call psb_erractionsave(err_act)
|
|
||||||
if (psb_errstatus_fatal()) then
|
|
||||||
info = psb_err_internal_error_; goto 9999
|
|
||||||
end if
|
|
||||||
ma = a%get_nrows()
|
|
||||||
mb = b%get_nrows()
|
|
||||||
|
|
||||||
select case(ialg)
|
|
||||||
case(mld_ilu_n_,mld_milu_n_)
|
|
||||||
! Ok
|
|
||||||
case default
|
|
||||||
info=psb_err_input_asize_invalid_i_
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione,ialg,izero,izero,izero/))
|
|
||||||
goto 9999
|
|
||||||
end select
|
|
||||||
|
|
||||||
call trw%allocate(izero,izero,ione)
|
|
||||||
if(info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='psb_sp_all'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
m = ma+mb
|
|
||||||
|
|
||||||
if (psb_toupper(upd) == 'F' ) then
|
|
||||||
lirp(1) = 1
|
|
||||||
uirp(1) = 1
|
|
||||||
l1 = 0
|
|
||||||
l2 = 0
|
|
||||||
|
|
||||||
!
|
|
||||||
! Cycle over the matrix rows
|
|
||||||
!
|
|
||||||
do i = 1, m
|
|
||||||
|
|
||||||
d(i) = szero
|
|
||||||
|
|
||||||
if (i <= ma) then
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in a,
|
|
||||||
! into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i,ma,a,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
else
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in b
|
|
||||||
! (as (i-ma)-th row), into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i-ma,mb,b,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
endif
|
|
||||||
|
|
||||||
lirp(i+1) = l1 + 1
|
|
||||||
uirp(i+1) = l2 + 1
|
|
||||||
|
|
||||||
dia = d(i)
|
|
||||||
do kk = lirp(i), lirp(i+1) - 1
|
|
||||||
!
|
|
||||||
! Compute entry l(i,k) (lower factor L) of the incomplete
|
|
||||||
! factorization
|
|
||||||
!
|
|
||||||
temp = lval(kk)
|
|
||||||
k = lja(kk)
|
|
||||||
lval(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 = uirp(i)
|
|
||||||
!
|
|
||||||
updateloop: do jj = uirp(k), uirp(k+1) - 1
|
|
||||||
!
|
|
||||||
j = uja(jj)
|
|
||||||
!
|
|
||||||
if (j < i) then
|
|
||||||
!
|
|
||||||
! search l(i,*) (i-th row of L) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low1, lirp(i+1) - 1
|
|
||||||
l = lja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low1 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
lval(ll) = lval(ll) - temp*uval(jj)
|
|
||||||
low1 = ll + 1
|
|
||||||
cycle updateloop
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
else if (j == i) then
|
|
||||||
!
|
|
||||||
! j=i: update the diagonal
|
|
||||||
!
|
|
||||||
dia = dia - temp*uval(jj)
|
|
||||||
cycle updateloop
|
|
||||||
!
|
|
||||||
else if (j > i) then
|
|
||||||
!
|
|
||||||
! search u(i,*) (i-th row of U) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low2, uirp(i+1) - 1
|
|
||||||
l = uja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low2 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
uval(ll) = uval(ll) - temp*uval(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*uval(jj)
|
|
||||||
end if
|
|
||||||
enddo updateloop
|
|
||||||
enddo
|
|
||||||
!
|
|
||||||
! Check the pivot size
|
|
||||||
!
|
|
||||||
if (abs(dia) < s_epstol) then
|
|
||||||
!
|
|
||||||
! Too small pivot: unstable factorization
|
|
||||||
!
|
|
||||||
info = psb_err_pivot_too_small_
|
|
||||||
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 = sone/dia
|
|
||||||
end if
|
|
||||||
d(i) = dia
|
|
||||||
!
|
|
||||||
! Scale row i of upper triangle
|
|
||||||
!
|
|
||||||
do kk = uirp(i), uirp(i+1) - 1
|
|
||||||
uval(kk) = uval(kk)*dia
|
|
||||||
enddo
|
|
||||||
enddo
|
|
||||||
else
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call trw%free()
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine mld_silu0_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: ilu_copyin
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_silu0_fact
|
|
||||||
!
|
|
||||||
! This routine copies a row of a sparse matrix A, stored in the psb_sspmat_type
|
|
||||||
! data structure a, into the arrays lval and uval 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 lval and uval are stored
|
|
||||||
! according to the CSR format; the corresponding column indices are stored in
|
|
||||||
! the arrays lja and uja.
|
|
||||||
!
|
|
||||||
! 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 lval, dia, uval row by row, through successive calls to
|
|
||||||
! ilu_copyin.
|
|
||||||
!
|
|
||||||
! The routine is used by mld_silu0_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_sspmat_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 lval.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the lower triangle
|
|
||||||
! copied in lval row by row (see mld_silu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! lval - real(psb_spk_), dimension(:), input/output.
|
|
||||||
! The array where the entries of the row corresponding to the
|
|
||||||
! lower triangle are copied.
|
|
||||||
! dia - real(psb_spk_), output.
|
|
||||||
! The diagonal entry of the copied row.
|
|
||||||
! l2 - integer, input/output.
|
|
||||||
! Pointer to the last occupied entry of uval.
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the upper triangle
|
|
||||||
! copied in uval row by row (see mld_silu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! uval - real(psb_spk_), 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_sspmat_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,lja,lval,&
|
|
||||||
& dia,l2,uja,uval,ktrw,trw,upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
type(psb_sspmat_type), intent(in) :: a
|
|
||||||
type(psb_s_coo_sparse_mat), intent(inout) :: trw
|
|
||||||
integer(psb_ipk_), intent(in) :: i,m,jd,jmin,jmax
|
|
||||||
integer(psb_ipk_), intent(inout) :: ktrw,l1,l2
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:), uja(:)
|
|
||||||
real(psb_spk_), intent(inout) :: lval(:), uval(:), dia
|
|
||||||
character, intent(in) :: upd
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,info,irb, nz
|
|
||||||
integer(psb_ipk_), parameter :: nrb=40
|
|
||||||
character(len=20), parameter :: name='ilu_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
|
|
||||||
if (psb_toupper(upd) == 'F') then
|
|
||||||
|
|
||||||
select type(aa => a%a)
|
|
||||||
type is (psb_s_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)
|
|
||||||
! write(0,*)'KKKKK',k
|
|
||||||
if ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = aa%val(j)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = aa%val(j)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = aa%val(j)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
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 lval, dia, uval, through
|
|
||||||
! successive calls to ilu_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='csget'
|
|
||||||
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 ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = trw%val(ktrw)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = trw%val(ktrw)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = trw%val(ktrw)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
ktrw = ktrw + 1
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end select
|
|
||||||
|
|
||||||
else
|
|
||||||
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine ilu_copyin
|
|
||||||
|
|
||||||
end subroutine mld_silu0_fact
|
|
||||||
@ -1,969 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_siluk_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_siluk_fact
|
|
||||||
! Version: real
|
|
||||||
! Contains: mld_siluk_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 (= mld_ilu_n_);
|
|
||||||
! the MILU(k) one if ialg = 2 (= mld_milu_n_); other values are
|
|
||||||
! not allowed.
|
|
||||||
! a - type(psb_sspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! l - type(psb_sspmat_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_sspmat_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_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 mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
! blck - type(psb_sspmat_type), input, optional, target.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then blck does not contain any row.
|
|
||||||
!
|
|
||||||
subroutine mld_siluk_fact(fill_in,ialg,a,l,u,d,info,blck)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_s_ilu_fact_mod, mld_protect_name => mld_siluk_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
integer(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_sspmat_type),intent(in) :: a
|
|
||||||
type(psb_sspmat_type),intent(inout) :: l,u
|
|
||||||
type(psb_sspmat_type),intent(in), optional, target :: blck
|
|
||||||
real(psb_spk_), intent(inout) :: d(:)
|
|
||||||
! Local Variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
|
|
||||||
type(psb_sspmat_type), pointer :: blck_
|
|
||||||
type(psb_s_csr_sparse_mat) :: ll, uu
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_siluk_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
|
|
||||||
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 mld_siluk_factint(fill_in,ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,info)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_siluk_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: mld_siluk_factint
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_siluk_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 (= mld_milu_n_);
|
|
||||||
! the ILU(k) factorization otherwise.
|
|
||||||
! m - integer, output.
|
|
||||||
! The total number of rows of the local matrix to be factorized,
|
|
||||||
! i.e. ma+mb.
|
|
||||||
! a - type(psb_sspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that, if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! b - type(psb_sspmat_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_spk_), dimension(:), output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the incomplete
|
|
||||||
! factorization.
|
|
||||||
! laspk - real(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 - real(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 mld_siluk_factint(fill_in,ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,info)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
type(psb_sspmat_type),intent(in) :: a,b
|
|
||||||
integer(psb_ipk_),intent(inout) :: l1,l2,info
|
|
||||||
integer(psb_ipk_), allocatable, intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
|
|
||||||
real(psb_spk_), allocatable, intent(inout) :: lval(:),uval(:)
|
|
||||||
real(psb_spk_), intent(inout) :: d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: ma,mb,i, ktrw,err_act,nidx, m
|
|
||||||
integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:)
|
|
||||||
real(psb_spk_), allocatable :: row(:)
|
|
||||||
type(psb_i_heap) :: heap
|
|
||||||
type(psb_s_coo_sparse_mat) :: trw
|
|
||||||
character(len=20), parameter :: name='mld_siluk_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(mld_ilu_n_,mld_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(:) = szero
|
|
||||||
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) = szero
|
|
||||||
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)
|
|
||||||
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)
|
|
||||||
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 mld_siluk_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: iluk_copyin
|
|
||||||
! Version: real
|
|
||||||
! Note: internal subroutine of mld_siluk_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_siluk_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_sspmat_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 - real(psb_spk_), 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_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_sspmat_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_sspmat_type), intent(in) :: a
|
|
||||||
type(psb_s_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(:)
|
|
||||||
real(psb_spk_), intent(inout) :: row(:)
|
|
||||||
type(psb_i_heap), intent(inout) :: heap
|
|
||||||
|
|
||||||
! 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_s_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)
|
|
||||||
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)
|
|
||||||
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: real
|
|
||||||
! Note: internal subroutine of mld_siluk_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_siluk_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 - real(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 - real(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 mld_siluk_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 mld_siluk_factint), according to
|
|
||||||
! the CSR storage format.
|
|
||||||
! uval - real(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(:)
|
|
||||||
real(psb_spk_), intent(inout) :: row(:), uval(:),d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,lrwk,jj,lastk, iret
|
|
||||||
real(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) /= szero).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: real
|
|
||||||
! Note: internal subroutine of mld_siluk_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 == 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 lval and uval 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_siluk_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 - real(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 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 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 mld_siluk_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
|
|
||||||
! mld_siluk_factint), according to the CSR storage format.
|
|
||||||
! lval - real(psb_spk_), dimension(:), input/output.
|
|
||||||
! The array where the entries of the row corresponding to the
|
|
||||||
! L factor are copied.
|
|
||||||
! d - real(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 mld_siluk_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
|
|
||||||
! mld_zilu_fctint), according to the CSR storage format.
|
|
||||||
! uval - real(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(:)
|
|
||||||
real(psb_spk_), allocatable, intent(inout) :: uval(:), lval(:)
|
|
||||||
real(psb_spk_), intent(inout) :: row(:), d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: j,isz,err_act,int_err(5),idxp
|
|
||||||
character(len=20), parameter :: name='mld_siluk_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) = szero
|
|
||||||
|
|
||||||
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 == 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) = szero
|
|
||||||
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) = szero
|
|
||||||
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 == 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) = szero
|
|
||||||
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) = sone/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 mld_siluk_fact
|
|
||||||
File diff suppressed because it is too large
Load Diff
@ -1,666 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_zilu0_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_zilu0_fact
|
|
||||||
! Version: complex
|
|
||||||
! Contains: mld_zilu0_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_ziluk_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_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_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_zspmat_type), input/output.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! u - type(psb_zspmat_type), input/output.
|
|
||||||
! The U factor (except its diagonal) in the incomplete factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! d - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the incomplete
|
|
||||||
! factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
! blck - type(psb_zspmat_type), input, optional, target.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then blck is empty.
|
|
||||||
!
|
|
||||||
subroutine mld_zilu0_fact(ialg,a,l,u,d,info,blck, upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_z_ilu_fact_mod, mld_protect_name => mld_zilu0_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: ialg
|
|
||||||
type(psb_zspmat_type),intent(in) :: a
|
|
||||||
type(psb_zspmat_type),intent(inout) :: l,u
|
|
||||||
complex(psb_dpk_), intent(inout) :: d(:)
|
|
||||||
integer(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_zspmat_type),intent(in), optional, target :: blck
|
|
||||||
character, intent(in), optional :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
type(psb_zspmat_type), pointer :: blck_
|
|
||||||
type(psb_z_csr_sparse_mat) :: ll, uu
|
|
||||||
character :: upd_
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_zilu0_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
if (present(upd)) then
|
|
||||||
upd_ = psb_toupper(upd)
|
|
||||||
else
|
|
||||||
upd_ = 'F'
|
|
||||||
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(0) or the MILU(0) factorization, depending on ialg
|
|
||||||
!
|
|
||||||
call mld_zilu0_factint(ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,upd_,info)
|
|
||||||
if(info.ne.0) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_zilu0_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()
|
|
||||||
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
|
|
||||||
deallocate(blck_)
|
|
||||||
endif
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
contains
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: mld_zilu0_factint
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_zilu0_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 lval, uval, 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_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that, if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! mb - integer, input.
|
|
||||||
! The number of rows of the local submatrix stored into b.
|
|
||||||
! b - type(psb_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been
|
|
||||||
! reordered (see mld_fact_bld), then b does not contain any row.
|
|
||||||
! d - complex(psb_dpk_), dimension(:), output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the
|
|
||||||
! incomplete factorization.
|
|
||||||
! lval - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The entries of U are stored according to the CSR format.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the L factor,
|
|
||||||
! 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 in lval, according to the CSR storage format.
|
|
||||||
! uval - complex(psb_dpk_), 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 lval.
|
|
||||||
! l2 - integer, output.
|
|
||||||
! The number of nonzero entries in uval.
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
!
|
|
||||||
subroutine mld_zilu0_factint(ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,upd,info)
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: ialg
|
|
||||||
type(psb_zspmat_type),intent(in) :: a,b
|
|
||||||
integer(psb_ipk_),intent(inout) :: l1,l2,info
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:),lirp(:),uja(:),uirp(:)
|
|
||||||
complex(psb_dpk_), intent(inout) :: lval(:),uval(:),d(:)
|
|
||||||
character, intent(in) :: upd
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: i,j,k,l,low1,low2,kk,jj,ll, ktrw,err_act, m
|
|
||||||
integer(psb_ipk_) :: ma,mb
|
|
||||||
complex(psb_dpk_) :: dia,temp
|
|
||||||
integer(psb_ipk_), parameter :: nrb=16
|
|
||||||
type(psb_z_coo_sparse_mat) :: trw
|
|
||||||
integer(psb_ipk_) :: int_err(5)
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_zilu0_factint'
|
|
||||||
info=psb_success_
|
|
||||||
call psb_erractionsave(err_act)
|
|
||||||
if (psb_errstatus_fatal()) then
|
|
||||||
info = psb_err_internal_error_; goto 9999
|
|
||||||
end if
|
|
||||||
ma = a%get_nrows()
|
|
||||||
mb = b%get_nrows()
|
|
||||||
|
|
||||||
select case(ialg)
|
|
||||||
case(mld_ilu_n_,mld_milu_n_)
|
|
||||||
! Ok
|
|
||||||
case default
|
|
||||||
info=psb_err_input_asize_invalid_i_
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione,ialg,izero,izero,izero/))
|
|
||||||
goto 9999
|
|
||||||
end select
|
|
||||||
|
|
||||||
call trw%allocate(izero,izero,ione)
|
|
||||||
if(info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='psb_sp_all'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
m = ma+mb
|
|
||||||
|
|
||||||
if (psb_toupper(upd) == 'F' ) then
|
|
||||||
lirp(1) = 1
|
|
||||||
uirp(1) = 1
|
|
||||||
l1 = 0
|
|
||||||
l2 = 0
|
|
||||||
|
|
||||||
!
|
|
||||||
! Cycle over the matrix rows
|
|
||||||
!
|
|
||||||
do i = 1, m
|
|
||||||
|
|
||||||
d(i) = zzero
|
|
||||||
|
|
||||||
if (i <= ma) then
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in a,
|
|
||||||
! into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i,ma,a,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
else
|
|
||||||
!
|
|
||||||
! Copy the i-th local row of the matrix, stored in b
|
|
||||||
! (as (i-ma)-th row), into lval/d(i)/uval
|
|
||||||
!
|
|
||||||
call ilu_copyin(i-ma,mb,b,i,ione,m,l1,lja,lval,&
|
|
||||||
& d(i),l2,uja,uval,ktrw,trw,upd)
|
|
||||||
endif
|
|
||||||
|
|
||||||
lirp(i+1) = l1 + 1
|
|
||||||
uirp(i+1) = l2 + 1
|
|
||||||
|
|
||||||
dia = d(i)
|
|
||||||
do kk = lirp(i), lirp(i+1) - 1
|
|
||||||
!
|
|
||||||
! Compute entry l(i,k) (lower factor L) of the incomplete
|
|
||||||
! factorization
|
|
||||||
!
|
|
||||||
temp = lval(kk)
|
|
||||||
k = lja(kk)
|
|
||||||
lval(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 = uirp(i)
|
|
||||||
!
|
|
||||||
updateloop: do jj = uirp(k), uirp(k+1) - 1
|
|
||||||
!
|
|
||||||
j = uja(jj)
|
|
||||||
!
|
|
||||||
if (j < i) then
|
|
||||||
!
|
|
||||||
! search l(i,*) (i-th row of L) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low1, lirp(i+1) - 1
|
|
||||||
l = lja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low1 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
lval(ll) = lval(ll) - temp*uval(jj)
|
|
||||||
low1 = ll + 1
|
|
||||||
cycle updateloop
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
else if (j == i) then
|
|
||||||
!
|
|
||||||
! j=i: update the diagonal
|
|
||||||
!
|
|
||||||
dia = dia - temp*uval(jj)
|
|
||||||
cycle updateloop
|
|
||||||
!
|
|
||||||
else if (j > i) then
|
|
||||||
!
|
|
||||||
! search u(i,*) (i-th row of U) for a matching index j
|
|
||||||
!
|
|
||||||
do ll = low2, uirp(i+1) - 1
|
|
||||||
l = uja(ll)
|
|
||||||
if (l > j) then
|
|
||||||
low2 = ll
|
|
||||||
exit
|
|
||||||
else if (l == j) then
|
|
||||||
uval(ll) = uval(ll) - temp*uval(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*uval(jj)
|
|
||||||
end if
|
|
||||||
enddo updateloop
|
|
||||||
enddo
|
|
||||||
!
|
|
||||||
! Check the pivot size
|
|
||||||
!
|
|
||||||
if (abs(dia) < d_epstol) then
|
|
||||||
!
|
|
||||||
! Too small pivot: unstable factorization
|
|
||||||
!
|
|
||||||
info = psb_err_pivot_too_small_
|
|
||||||
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 = zone/dia
|
|
||||||
end if
|
|
||||||
d(i) = dia
|
|
||||||
!
|
|
||||||
! Scale row i of upper triangle
|
|
||||||
!
|
|
||||||
do kk = uirp(i), uirp(i+1) - 1
|
|
||||||
uval(kk) = uval(kk)*dia
|
|
||||||
enddo
|
|
||||||
enddo
|
|
||||||
else
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call trw%free()
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine mld_zilu0_factint
|
|
||||||
|
|
||||||
!
|
|
||||||
! Subroutine: ilu_copyin
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_zilu0_fact
|
|
||||||
!
|
|
||||||
! This routine copies a row of a sparse matrix A, stored in the psb_zspmat_type
|
|
||||||
! data structure a, into the arrays lval and uval 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 lval and uval are stored
|
|
||||||
! according to the CSR format; the corresponding column indices are stored in
|
|
||||||
! the arrays lja and uja.
|
|
||||||
!
|
|
||||||
! 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 lval, dia, uval row by row, through successive calls to
|
|
||||||
! ilu_copyin.
|
|
||||||
!
|
|
||||||
! The routine is used by mld_zilu0_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_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the row to be copied.
|
|
||||||
! jd - integer, input.
|
|
||||||
! The column index of the diagonal entry of the row to be
|
|
||||||
! copied.
|
|
||||||
! jmin - integer, input.
|
|
||||||
! 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 lval.
|
|
||||||
! lja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the lower triangle
|
|
||||||
! copied in lval row by row (see mld_zilu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! lval - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The array where the entries of the row corresponding to the
|
|
||||||
! lower triangle are copied.
|
|
||||||
! dia - complex(psb_dpk_), output.
|
|
||||||
! The diagonal entry of the copied row.
|
|
||||||
! l2 - integer, input/output.
|
|
||||||
! Pointer to the last occupied entry of uval.
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the upper triangle
|
|
||||||
! copied in uval row by row (see mld_zilu0_factint), according
|
|
||||||
! to the CSR storage format.
|
|
||||||
! uval - complex(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_zspmat_type), input/output.
|
|
||||||
! A staging buffer. If the matrix A is not in CSR format, we use
|
|
||||||
! the psb_sp_getblk routine and store its output in trw; when we
|
|
||||||
! need to call psb_sp_getblk we do it for a block of rows, and then
|
|
||||||
! we consume them from trw in successive calls to this routine,
|
|
||||||
! until we empty the buffer. Thus we will make a call to psb_sp_getblk
|
|
||||||
! every nrb calls to copyin. If A is in CSR format it is unused.
|
|
||||||
!
|
|
||||||
subroutine ilu_copyin(i,m,a,jd,jmin,jmax,l1,lja,lval,&
|
|
||||||
& dia,l2,uja,uval,ktrw,trw,upd)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
type(psb_zspmat_type), intent(in) :: a
|
|
||||||
type(psb_z_coo_sparse_mat), intent(inout) :: trw
|
|
||||||
integer(psb_ipk_), intent(in) :: i,m,jd,jmin,jmax
|
|
||||||
integer(psb_ipk_), intent(inout) :: ktrw,l1,l2
|
|
||||||
integer(psb_ipk_), intent(inout) :: lja(:), uja(:)
|
|
||||||
complex(psb_dpk_), intent(inout) :: lval(:), uval(:), dia
|
|
||||||
character, intent(in) :: upd
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,info,irb, nz
|
|
||||||
integer(psb_ipk_), parameter :: nrb=40
|
|
||||||
character(len=20), parameter :: name='ilu_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
|
|
||||||
if (psb_toupper(upd) == 'F') then
|
|
||||||
|
|
||||||
select type(aa => a%a)
|
|
||||||
type is (psb_z_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)
|
|
||||||
! write(0,*)'KKKKK',k
|
|
||||||
if ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = aa%val(j)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = aa%val(j)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = aa%val(j)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
enddo
|
|
||||||
|
|
||||||
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 lval, dia, uval, through
|
|
||||||
! successive calls to ilu_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='csget'
|
|
||||||
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 ((k < jd).and.(k >= jmin)) then
|
|
||||||
l1 = l1 + 1
|
|
||||||
lval(l1) = trw%val(ktrw)
|
|
||||||
lja(l1) = k
|
|
||||||
else if (k == jd) then
|
|
||||||
dia = trw%val(ktrw)
|
|
||||||
else if ((k > jd).and.(k <= jmax)) then
|
|
||||||
l2 = l2 + 1
|
|
||||||
uval(l2) = trw%val(ktrw)
|
|
||||||
uja(l2) = k
|
|
||||||
end if
|
|
||||||
ktrw = ktrw + 1
|
|
||||||
enddo
|
|
||||||
|
|
||||||
end select
|
|
||||||
|
|
||||||
else
|
|
||||||
|
|
||||||
write(0,*) 'Update not implemented '
|
|
||||||
info = 31
|
|
||||||
call psb_errpush(info,name,&
|
|
||||||
& i_err=(/ione*13,izero,izero,izero,izero/),a_err=upd)
|
|
||||||
goto 9999
|
|
||||||
|
|
||||||
end if
|
|
||||||
|
|
||||||
call psb_erractionrestore(err_act)
|
|
||||||
return
|
|
||||||
|
|
||||||
9999 call psb_error_handler(err_act)
|
|
||||||
|
|
||||||
return
|
|
||||||
|
|
||||||
end subroutine ilu_copyin
|
|
||||||
|
|
||||||
end subroutine mld_zilu0_fact
|
|
||||||
@ -1,969 +0,0 @@
|
|||||||
!
|
|
||||||
!
|
|
||||||
! 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: mld_ziluk_fact.f90
|
|
||||||
!
|
|
||||||
! Subroutine: mld_ziluk_fact
|
|
||||||
! Version: complex
|
|
||||||
! Contains: mld_ziluk_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 (= mld_ilu_n_);
|
|
||||||
! the MILU(k) one if ialg = 2 (= mld_milu_n_); other values are
|
|
||||||
! not allowed.
|
|
||||||
! a - type(psb_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! l - type(psb_zspmat_type), input/output.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! u - type(psb_zspmat_type), input/output.
|
|
||||||
! The U factor (except its diagonal) in the incomplete factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! d - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the incomplete
|
|
||||||
! factorization.
|
|
||||||
! Note: its allocation is managed by the calling routine mld_ilu_bld,
|
|
||||||
! hence it cannot be only intent(out).
|
|
||||||
! info - integer, output.
|
|
||||||
! Error code.
|
|
||||||
! blck - type(psb_zspmat_type), input, optional, target.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then blck does not contain any row.
|
|
||||||
!
|
|
||||||
subroutine mld_ziluk_fact(fill_in,ialg,a,l,u,d,info,blck)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
use mld_z_ilu_fact_mod, mld_protect_name => mld_ziluk_fact
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
integer(psb_ipk_), intent(out) :: info
|
|
||||||
type(psb_zspmat_type),intent(in) :: a
|
|
||||||
type(psb_zspmat_type),intent(inout) :: l,u
|
|
||||||
type(psb_zspmat_type),intent(in), optional, target :: blck
|
|
||||||
complex(psb_dpk_), intent(inout) :: d(:)
|
|
||||||
! Local Variables
|
|
||||||
integer(psb_ipk_) :: l1, l2, m, err_act
|
|
||||||
|
|
||||||
type(psb_zspmat_type), pointer :: blck_
|
|
||||||
type(psb_z_csr_sparse_mat) :: ll, uu
|
|
||||||
character(len=20) :: name, ch_err
|
|
||||||
|
|
||||||
name='mld_ziluk_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_%csall(izero,izero,info,ione)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='csall'
|
|
||||||
call psb_errpush(info,name,a_err=ch_err)
|
|
||||||
goto 9999
|
|
||||||
end if
|
|
||||||
endif
|
|
||||||
|
|
||||||
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 mld_ziluk_factint(fill_in,ialg,a,blck_,&
|
|
||||||
& d,ll%val,ll%ja,ll%irp,uu%val,uu%ja,uu%irp,l1,l2,info)
|
|
||||||
if (info /= psb_success_) then
|
|
||||||
info=psb_err_from_subroutine_
|
|
||||||
ch_err='mld_ziluk_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: mld_ziluk_factint
|
|
||||||
! Version: complex
|
|
||||||
! Note: internal subroutine of mld_ziluk_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 (= mld_milu_n_);
|
|
||||||
! the ILU(k) factorization otherwise.
|
|
||||||
! m - integer, output.
|
|
||||||
! The total number of rows of the local matrix to be factorized,
|
|
||||||
! i.e. ma+mb.
|
|
||||||
! a - type(psb_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the local matrix.
|
|
||||||
! Note that, if the 'base' Additive Schwarz preconditioner
|
|
||||||
! has overlap greater than 0 and the matrix has not been reordered
|
|
||||||
! (see mld_fact_bld), then a contains only the 'original' local part
|
|
||||||
! of the distributed matrix, i.e. the rows of the matrix held
|
|
||||||
! by the calling process according to the initial data distribution.
|
|
||||||
! b - type(psb_zspmat_type), input.
|
|
||||||
! The sparse matrix structure containing the remote rows of the
|
|
||||||
! distributed matrix, that have been retrieved by mld_as_bld
|
|
||||||
! to build an Additive Schwarz base preconditioner with overlap
|
|
||||||
! greater than 0. If the overlap is 0 or the matrix has been reordered
|
|
||||||
! (see mld_fact_bld), then b does not contain any row.
|
|
||||||
! d - complex(psb_dpk_), dimension(:), output.
|
|
||||||
! The inverse of the diagonal entries of the U factor in the incomplete
|
|
||||||
! factorization.
|
|
||||||
! laspk - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The L factor in the incomplete factorization.
|
|
||||||
! lia1 - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the L factor,
|
|
||||||
! according to the CSR storage format.
|
|
||||||
! lia2 - integer, dimension(:), input/output.
|
|
||||||
! The indices identifying the first nonzero entry of each row
|
|
||||||
! of the L factor in laspk, according to the CSR storage format.
|
|
||||||
! uval - complex(psb_dpk_), 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 mld_ziluk_factint(fill_in,ialg,a,b,&
|
|
||||||
& d,lval,lja,lirp,uval,uja,uirp,l1,l2,info)
|
|
||||||
|
|
||||||
use psb_base_mod
|
|
||||||
|
|
||||||
implicit none
|
|
||||||
|
|
||||||
! Arguments
|
|
||||||
integer(psb_ipk_), intent(in) :: fill_in, ialg
|
|
||||||
type(psb_zspmat_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_dpk_), allocatable, intent(inout) :: lval(:),uval(:)
|
|
||||||
complex(psb_dpk_), intent(inout) :: d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: ma,mb,i, ktrw,err_act,nidx, m
|
|
||||||
integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:)
|
|
||||||
complex(psb_dpk_), allocatable :: row(:)
|
|
||||||
type(psb_i_heap) :: heap
|
|
||||||
type(psb_z_coo_sparse_mat) :: trw
|
|
||||||
character(len=20), parameter :: name='mld_ziluk_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(mld_ilu_n_,mld_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(:) = 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,ione,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,ione,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 == 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 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(psb_dpk_), 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_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_zspmat_type), input/output.
|
|
||||||
! A staging buffer. If the matrix A is not in CSR format, we use
|
|
||||||
! the psb_sp_getblk routine and store its output in trw; when we
|
|
||||||
! need to call psb_sp_getblk we do it for a block of rows, and then
|
|
||||||
! we consume them from trw in successive calls to this routine,
|
|
||||||
! until we empty the buffer. Thus we will make a call to psb_sp_getblk
|
|
||||||
! every nrb calls to copyin. If A is in CSR format it is unused.
|
|
||||||
!
|
|
||||||
subroutine 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_z_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_dpk_), intent(inout) :: row(:)
|
|
||||||
type(psb_i_heap), intent(inout) :: heap
|
|
||||||
|
|
||||||
! 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_z_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)
|
|
||||||
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)
|
|
||||||
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 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(psb_dpk_), dimension(:), input/output.
|
|
||||||
! In input it contains the row to which the elimination step
|
|
||||||
! has to be applied. In output it contains the row after the
|
|
||||||
! elimination step. It actually contains a full row, i.e.
|
|
||||||
! it contains also the zero entries of the row.
|
|
||||||
! 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_dpk_), 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 mld_ziluk_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 mld_ziluk_factint), according to
|
|
||||||
! the CSR storage format.
|
|
||||||
! uval - complex(psb_dpk_), dimension(:), input.
|
|
||||||
! The entries of the U factor above the current row (except the
|
|
||||||
! diagonal ones), stored according to the CSR format.
|
|
||||||
! 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_dpk_), intent(inout) :: row(:), uval(:),d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: k,j,lrwk,jj,lastk, iret
|
|
||||||
complex(psb_dpk_) :: 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) /= 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=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 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 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 == 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 lval and uval 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(psb_dpk_), dimension(:), input/output.
|
|
||||||
! It contains, input, the row to be copied, and, in output,
|
|
||||||
! the null vector (the latter is used in the next call to
|
|
||||||
! 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 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 mld_ziluk_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
|
|
||||||
! mld_ziluk_factint), according to the CSR storage format.
|
|
||||||
! lval - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The array where the entries of the row corresponding to the
|
|
||||||
! L factor are copied.
|
|
||||||
! d - complex(psb_dpk_), dimension(:), input/output.
|
|
||||||
! The array where the inverse of the diagonal entry of the
|
|
||||||
! row is copied (only d(i) is used by the routine).
|
|
||||||
! uja - integer, dimension(:), input/output.
|
|
||||||
! The column indices of the nonzero entries of the U factor
|
|
||||||
! copied in uval row by row (see mld_ziluk_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
|
|
||||||
! mld_zilu_fctint), according to the CSR storage format.
|
|
||||||
! uval - complex(psb_dpk_), 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_dpk_), allocatable, intent(inout) :: uval(:), lval(:)
|
|
||||||
complex(psb_dpk_), intent(inout) :: row(:), d(:)
|
|
||||||
|
|
||||||
! Local variables
|
|
||||||
integer(psb_ipk_) :: j,isz,err_act,int_err(5),idxp
|
|
||||||
character(len=20), parameter :: name='mld_ziluk_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) = zzero
|
|
||||||
|
|
||||||
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 == 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(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 == 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
|
|
||||||
! lval and uval
|
|
||||||
!
|
|
||||||
lirp(i+1) = l1 + 1
|
|
||||||
uirp(i+1) = l2 + 1
|
|
||||||
|
|
||||||
!
|
|
||||||
! Check the pivot size
|
|
||||||
!
|
|
||||||
if (abs(d(i)) < d_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) = zone/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 mld_ziluk_fact
|
|
||||||
File diff suppressed because it is too large
Load Diff
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Reference in New Issue