!!$
!!$
!!$ MLD2P4 version 1.0
!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
!!$ based on PSBLAS (Parallel Sparse BLAS version 2.2)
!!$
!!$ (C) Copyright 2008
!!$
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari University of Rome Tor Vergata
!!$ Pasqua D'Ambra ICAR-CNR, Naples
!!$ Daniela di Serafino Second University of Naples
!!$
!!$ Redistribution and use in source and binary forms, with or without
!!$ modification, are permitted provided that the following conditions
!!$ are met:
!!$ 1. Redistributions of source code must retain the above copyright
!!$ notice, this list of conditions and the following disclaimer.
!!$ 2. Redistributions in binary form must reproduce the above copyright
!!$ notice, this list of conditions, and the following disclaimer in the
!!$ documentation and/or other materials provided with the distribution.
!!$ 3. The name of the MLD2P4 group or the names of its contributors may
!!$ not be used to endorse or promote products derived from this
!!$ software without specific written permission.
!!$
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
!!$ POSSIBILITY OF SUCH DAMAGE.
!!$
!!$
! File mld_ssub_solve.f90
!
! Subroutine: mld_ssub_solve
! Version: real
!
! This routine computes
!
! Y = beta*Y + alpha*op(K^(-1))*X,
!
! where
! - K is a factored matrix, as specified below,
! - op(K^(-1)) is K^(-1) or its transpose, according to the value of the
! argument trans,
! - X and Y are vectors,
! - alpha and beta are scalars.
!
! Depending on K, alpha and beta (and on the communication descriptor desc_data
! - see the arguments below), the above computation may correspond to one of
! the following tasks:
!
! 1. approximate solution of a linear system
!
! A*Y = X,
!
! by using the L and U factors computed with an ILU (incomplete LU) factorization
! of A. In this case K = L*U ~ A, alpha = 1 and beta = 0. The factors L and U
! (and the matrix A) are either distributed and block-diagonal or replicated.
!
! 2. Solution of a linear system
!
! A*Y = X,
!
! by using the L and U factors computed with a LU factorization of A. In this
! case K = L*U = A, alpha = 1 and beta = 0. The LU factorization is performed
! by one of the following auxiliary pakages:
! a. UMFPACK,
! b. SuperLU,
! c. SuperLU_Dist.
! In the cases a. and b., the factors L and U (and the matrix A) are either
! distributed and block diagonal) or replicated; in the case c., L, U (and A)
! are distributed.
!
! This routine is used by mld_ssub_aply, to apply a 'base' block-Jacobi or
! Additive Schwarz (AS) preconditioner at any level of a multilevel preconditioner,
! or a block-Jacobi or LU or ILU solver at the coarsest level of a multilevel
! preconditioner.
!
!
! Arguments:
!
! alpha - real(psb_spk_), input.
! The scalar alpha.
! prec - type(mld_sbaseprec_type), input.
! The 'base preconditioner' data structure containing the local
! part of the L and U factors of the matrix A.
! x - real(psb_spk_), dimension(:), input.
! The local part of the vector X.
! beta - real(psb_spk_), input.
! The scalar beta.
! y - real(psb_spk_), dimension(:), input/output.
! The local part of the vector Y.
! desc_data - type(psb_desc_type), input.
! The communication descriptor associated to the matrix to be
! preconditioned or 'inverted'.
! trans - character(len=1), input.
! If trans='N','n' then op(K^(-1)) = K^(-1);
! if trans='T','t' then op(K^(-1)) = K^(-T) (transpose of K^(-1)).
! If prec%iprcparm(mld_smoother_sweeps_) > 1, the value of trans provided
! in input is ignored.
! work - real(psb_spk_), dimension (:), target.
! Workspace. Its size must be at least 4*psb_cd_get_local_cols(desc_data).
! info - integer, output.
! Error code.
!
subroutine mld_ssub_solve(alpha,prec,x,beta,y,desc_data,trans,work,info)
use psb_base_mod
use mld_inner_mod, mld_protect_name => mld_ssub_solve
implicit none
! Arguments
type(psb_desc_type), intent(in) :: desc_data
type(mld_sbaseprc_type), intent(in) :: prec
real(psb_spk_),intent(in) :: x(:)
real(psb_spk_),intent(inout) :: y(:)
real(psb_spk_),intent(in) :: alpha,beta
character(len=1),intent(in) :: trans
real(psb_spk_),target, intent(inout) :: work(:)
integer, intent(out) :: info
! Local variables
integer :: n_row,n_col
real(psb_spk_), pointer :: ww(:), aux(:), tx(:),ty(:)
integer :: ictxt,np,me,i, err_act
character(len=20) :: name
character :: trans_
interface
subroutine mld_sumf_solve(flag,m,x,b,n,ptr,info)
use psb_base_mod
integer, intent(in) :: flag,m,n,ptr
integer, intent(out) :: info
real(psb_spk_), intent(in) :: b(*)
real(psb_spk_), intent(inout) :: x(*)
end subroutine mld_sumf_solve
end interface
name='mld_ssub_solve'
info = 0
call psb_erractionsave(err_act)
ictxt=psb_cd_get_context(desc_data)
call psb_info(ictxt, me, np)
trans_ = psb_toupper(trans)
select case(trans_)
case('N')
case('T','C')
case default
call psb_errpush(40,name)
goto 9999
end select
n_row = psb_cd_get_local_rows(desc_data)
n_col = psb_cd_get_local_cols(desc_data)
if (n_col <= size(work)) then
ww => work(1:n_col)
if ((4*n_col+n_col) <= size(work)) then
aux => work(n_col+1:)
else
allocate(aux(4*n_col),stat=info)
if (info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/4*n_col,0,0,0,0/),&
& a_err='real(psb_spk_)')
goto 9999
end if
endif
else
allocate(ww(n_col),aux(4*n_col),stat=info)
if (info /= 0) then
info=4025
call psb_errpush(info,name,i_err=(/5*n_col,0,0,0,0/),&
& a_err='real(psb_spk_)')
goto 9999
end if
endif
select case(prec%iprcparm(mld_sub_solve_))
case(mld_ilu_n_,mld_milu_n_,mld_ilu_t_)
!
! Apply a block-Jacobi preconditioner with ILU(k)/MILU(k)/ILU(k,t)
! factorization of the blocks (distributed matrix) or approximately
! solve a system through ILU(k)/MILU(k)/ILU(k,t) (replicated matrix).
!
select case(trans_)
case('N')
call psb_spsm(sone,prec%av(mld_l_pr_),x,szero,ww,desc_data,info,&
& trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux)
if (info == 0) call psb_spsm(alpha,prec%av(mld_u_pr_),ww,beta,y,desc_data,info,&
& trans=trans_,unit='U',choice=psb_none_, work=aux)
case('T','C')
call psb_spsm(sone,prec%av(mld_u_pr_),x,szero,ww,desc_data,info,&
& trans=trans_,unit='L',diag=prec%d,choice=psb_none_,work=aux)
if (info == 0) call psb_spsm(alpha,prec%av(mld_l_pr_),ww,beta,y,desc_data,info,&
& trans=trans_,unit='U',choice=psb_none_,work=aux)
case default
call psb_errpush(4001,name,a_err='Invalid TRANS in ILU subsolve')
goto 9999
end select
case(mld_slu_)
!
! Apply a block-Jacobi preconditioner with LU factorization of the
! blocks (distributed matrix) or approximately solve a local linear
! system through LU (replicated matrix). The SuperLU package is used
! to apply the LU factorization in both cases.
!
ww(1:n_row) = x(1:n_row)
select case(trans_)
case('N')
call mld_sslu_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info)
case('T','C')
call mld_sslu_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slu_ptr_),info)
case default
call psb_errpush(4001,name,a_err='Invalid TRANS in SLU subsolve')
goto 9999
end select
if (info ==0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info)
case(mld_sludist_)
!
! Solve a distributed linear system with the LU factorization.
! The SuperLU_DIST package is used.
!
ww(1:n_row) = x(1:n_row)
select case(trans_)
case('N')
call mld_ssludist_solve(0,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info)
case('T','C')
call mld_ssludist_solve(1,n_row,1,ww,n_row,prec%iprcparm(mld_slud_ptr_),info)
case default
call psb_errpush(4001,name,a_err='Invalid TRANS in SLUDist subsolve')
goto 9999
end select
if (info == 0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info)
case (mld_umf_)
!
! Apply a block-Jacobi preconditioner with LU factorization of the
! blocks (distributed matrix) or approximately solve a local linear
! system through LU (replicated matrix). The UMFPACK package is used
! to apply the LU factorization in both cases.
!
select case(trans_)
case('N')
call mld_sumf_solve(0,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info)
case('T','C')
call mld_sumf_solve(1,n_row,ww,x,n_row,prec%iprcparm(mld_umf_numptr_),info)
case default
call psb_errpush(4001,name,a_err='Invalid TRANS in UMF subsolve')
goto 9999
end select
if (info == 0) call psb_geaxpby(alpha,ww,beta,y,desc_data,info)
case default
call psb_errpush(4001,name,a_err='Invalid mld_sub_solve_')
goto 9999
end select
if (info /= 0) then
call psb_errpush(4001,name,a_err='Error in subsolve')
goto 9999
endif
if (n_col <= size(work)) then
if ((4*n_col+n_col) <= size(work)) then
else
deallocate(aux)
endif
else
deallocate(ww,aux)
endif
call psb_erractionrestore(err_act)
return
9999 continue
call psb_erractionrestore(err_act)
if (err_act.eq.psb_act_abort_) then
call psb_error()
return
end if
return
end subroutine mld_ssub_solve