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426 lines
21 KiB
TeX
426 lines
21 KiB
TeX
\section{User Interface\label{sec:userinterface}}
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\markboth{\textsc{MLD2P4 User's and Reference Guide}}
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{\textsc{\ref{sec:userinterface} User Interface}}
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The basic user interface of MLD2P4 consists of six routines. The four routines \verb|mld_precinit|,
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\verb|mld_precset|, \verb|mld_precbld| and \verb|mld_precaply| encapsulate all the functionalities
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for the setup and the application of any one-level and multi-level
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preconditioner implemented in the package.
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The routine \verb|mld_precfree| deallocates the preconditioner data structure, while
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\verb|mld_precdescr| prints a description of the preconditioner setup by the user.
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For each routine, the same user interface is overloaded with
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respect to the real/complex case and the single/double precision;
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arguments with appropriate data types must be passed to the routine,
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i.e.
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\begin{itemize}
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\item the sparse matrix data structure, containing the matrix to be
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preconditioned, must be of type \verb|mld_|\emph{x}\verb|spmat_type|
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with \emph{x} = \verb|s| for real single precision, \emph{x} = \verb|d|
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for real double precision, \emph{x} = \verb|c| for complex single precision,
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\emph{x} = \verb|z| for complex double precision;
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\item the preconditioner data structure must be of type
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\verb|mld_|\emph{x}\verb|prec_type|, with \emph{x} =
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\verb|s|, \verb|d|, \verb|c|, \verb|z|, according to the sparse
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matrix data structure;
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\item the arrays containing the vectors $v$ and $w$ involved in
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the preconditioner application $w=M^{-1}v$ must be of type
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\emph{type}\verb|(|\emph{kind\_parameter}\verb|)|, with \emph{type} =
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\verb|real|, \verb|complex| and \emph{kind\_parameter} = \verb|kind(1.e0)|,
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\verb|kind(1.d0)|, according to the sparse matrix and preconditioner
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data structure; note that the PSBLAS module \verb|psb_base_mod|
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provides the constants \verb|psb_spk_|
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= \verb|kind(1.e0)| and \verb|psb_dpk_| = \verb|kind(1.d0)|;
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\item real parameters defining the preconditioner must be declared
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according to the precision of the sparse matrix and preconditioner
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data structures (see Section~\ref{sec:precset}).
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\end{itemize}
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A description of each routine is given in the remainder of this section.
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\subsection{Subroutine mld\_precinit\label{sec:precinit}}
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\begin{center}
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\verb|mld_precinit(p,ptype,info)| \\
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\verb|mld_precinit(p,ptype,info,nlev)| \\
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\end{center}
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\noindent
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This routine allocates and initializes the preconditioner data structure,
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according to the preconditioner type chosen by the user.
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\subsubsection*{Arguments}
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\begin{tabular}{p{1.2cm}p{10.5cm}}
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\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
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& The preconditioner data structure. Note that \emph{x}
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must be chosen according to the real/complex, single/double
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precision version of MLD2P4 under use.\\
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\verb|ptype| & \verb|character(len=*), intent(in)|.\\
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& The type of preconditioner. Its values are specified
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in Table~\ref{tab:precinit}.\\
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& Note that the strings are case insensitive.\\
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\verb|info| & \verb|integer, intent(out)|.\\
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& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
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\verb|nlev| & \verb|integer, optional, intent(in)|.\\
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& The number of levels of the multilevel preconditioner.
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If \verb|nlev| is not present and \verb|ptype|=\verb|'ML'|, \verb|'ml'|,
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then \verb|nlev|=2 is assumed. Otherwise, \verb|nlev| is ignored.\\
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\end{tabular}
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\subsection{Subroutine mld\_precset\label{sec:precset}}
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\begin{center}
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\verb|mld_precset(p,what,val,info)|\\
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\end{center}
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\noindent
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This routine sets the parameters defining the preconditioner. More
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precisely, the parameter identified by \verb|what| is assigned the value
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contained in \verb|val|.
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\subsubsection*{Arguments}
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\begin{tabular}{p{1.2cm}p{10.5cm}}
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\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
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& The preconditioner data structure. Note that \emph{x} must
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be chosen according to the real/complex, single/double precision
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version of MLD2P4 under use.\\
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\verb|what| & \verb|integer, intent(in)|. \\
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& The number identifying the parameter to be set.
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A mnemonic constant has been associated to each of these
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numbers, as reported in Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.\\
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\verb|val | & \verb|integer| \emph{or} \verb|character(len=*)| \emph{or}
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\verb|real(psb_spk_)| \emph{or} \verb|real(psb_dpk_)|,
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\verb|intent(in)|.\\
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& The value of the parameter to be set. The list of allowed
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values and the corresponding data types is given in
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Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
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When the value is of type \verb|character(len=*)|,
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it is also treated as case insensitive.\\
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\verb|info| & \verb|integer, intent(out)|.\\
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& Error code. If no error, 0 is returned. See Section~\ref{sec:errors}
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for details.\\
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%
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%\verb|ilev| & \verb|integer, optional, intent(in)|.\\
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% & For the multilevel preconditioner, the level at which the
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% preconditioner parameter has to be set.
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% The levels are numbered in increasing
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% order starting from the finest one, i.e.\ level 1 is the finest level.
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% If \verb|ilev| is not present, the parameter identified by \verb|what|
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% is set at all the appropriate levels (see Table~\ref{tab:params}).
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\end{tabular}
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\ \\
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A variety of (one-level and multi-level) preconditioners can be obtained
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by a suitable setting of the preconditioner parameters. These parameters
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can be logically divided into four groups, i.e.\ parameters defining
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\begin{enumerate}
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\item the type of multi-level preconditioner;
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\item the one-level preconditioner used as smoother;
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\item the aggregation algorithm;
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\item the coarse-space correction at the coarsest level.
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\end{enumerate}
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A list of the parameters that can be set, along with their allowed and
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default values, is given in Tables~\ref{tab:p_type}-\ref{tab:p_coarse}.
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For a detailed description of the meaning of the parameters, please
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refer to Section~\ref{sec:background}.
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%
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%Note that the routine allows to set different features of the
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%preconditioner at each level through the use of \verb|ilev|.
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%This should be done by users with experience in the field of
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%multi-level preconditioners. Non-expert users are recommended
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%to call \verb| mld_precset| without specifying \verb|ilev|.
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\begin{sidewaystable}
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\begin{center}
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\begin{tabular}{|l|l|p{2cm}|l|p{7cm}|}
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\hline
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\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
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\textsc{comments} \\ \hline
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%\multicolumn{5}{|c|}{\emph{type of the multi-level preconditioner}}\\ \hline
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\verb|mld_ml_type_| & \verb|character(len=*)|
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& \texttt{'ADD'} \ \ \ \texttt{'MULT'}
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& \texttt{'MULT'}
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& Basic multi-level framework: additive or multiplicative
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among the levels (always additive inside a level). \\ \hline
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\verb|mld_smoother_type_|& \verb|character(len=*)|
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& \texttt{'DIAG'} \ \ \ \texttt{'BJAC'} \ \ \ \texttt{'AS'}
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& \texttt{'AS'}
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& Basic one-level preconditioner (i.e.\ smoother): diagonal,
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block Jacobi, AS \\ \hline
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\verb|mld_smoother_pos_| & \verb|character(len=*)|
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& \texttt{'PRE'} \ \ \ \texttt{'POST'} \ \ \ \texttt{'TWOSIDE'}
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& \texttt{'POST'}
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& ``Position'' of the smoother: pre-smoother, post-smoother,
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pre- and post-smoother. \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Parameters defining the type of multi-level preconditioner.
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\label{tab:p_type}}
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\end{sidewaystable}
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\begin{sidewaystable}
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\begin{center}
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\begin{tabular}{|l|l|p{3.2cm}|l|p{7cm}|}
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\hline
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\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
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\textsc{comments} \\ \hline
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%\multicolumn{5}{|c|}{\emph{basic one-level preconditioner (smoother)}} \\ \hline
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\verb|mld_sub_ovr_| & \verb|integer|
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& any integer number $\ge 0$
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& 1
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& Number of overlap layers. \\ \hline
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\verb|mld_sub_restr_| & \verb|character(len=*)|
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& \texttt{'HALO'} \hspace{2.5cm} \texttt{'NONE'}
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& \texttt{'HALO'}
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& Type of restriction operator:
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\texttt{'HALO'} for taking into account the overlap, \texttt{'NONE'}
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for neglecting it. \\ \hline
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\verb|mld_sub_prol_| & \verb|character(len=*)|
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& \texttt{'SUM'} \hspace{2.5cm} \texttt{'NONE'}
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& \texttt{'NONE'}
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& Type of prolongator operator:
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\texttt{'SUM'} for adding the contributions from the overlap, \texttt{'NONE'}
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for neglecting them. \\ \hline
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\verb|mld_sub_solve_| & \verb|character(len=*)|
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& \texttt{'ILU'} \hspace{2.5cm} \texttt{'MILU'} \hspace{2.5cm} \texttt{'ILUT'}
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\hspace{2.5cm} \texttt{'UMF'} \hspace{2.5cm} \texttt{'SLU'}
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& \texttt{'UMF'}
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& Local solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU
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(plus triangular solve). \\ \hline
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\verb|mld_sub_fillin_| & \verb|integer|
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& Any~int.~num.~$\ge 0$
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& 0
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& Fill-in level $p$ of the incomplete LU factorizations. \\ \hline
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\verb|mld_sub_iluthrs_| & \verb|real(|\emph{kind\_parameter}\verb|)|
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& Any~real~num.~$\ge 0$
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& \texttt{0.e0} (or \texttt{0.d0})
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& Drop tolerance $t$ in the ILU($p,t$) factorization. \\ \hline
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\verb|mld_sub_ren_| & \verb|character(len=*)|
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& \texttt{'RENUM\_NONE'} \texttt{'RENUM\_GLOBAL'} %, \texttt{'RENUM_GPS'}
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& \texttt{'RENUM\_NONE'}
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& Row and column reordering of the local submatrices: no reordering,
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reordering according to the global numbering of the rows and columns of
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the whole matrix. \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Parameters defining the one-level preconditioner used as smoother.
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\label{tab:p_smoother}}
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\end{sidewaystable}
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\begin{sidewaystable}
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\begin{center}
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\begin{tabular}{|l|l|p{2.3cm}|p{2.6cm}|p{7cm}|}
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\hline
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\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
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\textsc{comments} \\ \hline
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%\multicolumn{5}{|c|}{\emph{aggregation algorithm}} \\ \hline
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\verb|mld_aggr_alg_| & \verb|character(len=*)|
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& \texttt{'DEC'}
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& \texttt{'DEC'}
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& Aggregation algorithm. Currently, only the decoupled aggregation is available. \\ \hline
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\verb|mld_aggr_kind_| & \verb|character(len=*)|
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& \texttt{'SMOOTH'} \hspace{2.5cm} \texttt{'RAW'}
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& \texttt{'SMOOTH'}
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& Type of aggregation: smoothed or raw, i.e.\ using the tentative prolongator. \\ \hline
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\verb|mld_aggr_thresh_| & \verb|real(|\emph{kind\_parameter}\verb|)|
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& Any~real~num. $\in [0, 1]$
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& \texttt{0.e0} (or \texttt{0.d0})
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& The threshold $\theta$ in the aggregation algorithm. \\ \hline
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\verb|mld_aggr_eig_| & \verb|character(len=*)|
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& \texttt{'A\_NORMI'}
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& \texttt{'A\_NORMI'}
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& Estimate of the maximum eigenvalue of $D^{-1}A$
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for the smoothed aggregation. Currently, only the infinity norm of
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the matrix is available. \\ \hline
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\verb|mld_aggr_damp_| & \verb|real(|\emph{kind\_parameter}\verb|)|
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& Any~real~num. $>0$
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& \texttt{4.e0/3.e0} \hspace{1cm} (or \texttt{4.d0/3.d0})
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& The damping parameter $\omega$ in the aggregation algorithm. \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Parameters defining the aggregation algorithm.
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\label{tab:p_aggregation}}
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\end{sidewaystable}
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\begin{sidewaystable}
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\begin{center}
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\begin{tabular}{|l|l|p{3.2cm}|l|p{7cm}|}
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\hline
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\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
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\textsc{comments} \\ \hline
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%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline
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\verb|mld_coarse_mat_| & \verb|character(len=*)|
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& \texttt{'DISTR'} \hspace{2.5cm} \texttt{'REPL'}
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& \texttt{'DISTR'}
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& Coarsest matrix: distributed among the processors or replicated on each of them. \\ \hline
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\verb|mld_coarse_solve_| & \verb|character(len=*)|
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& \texttt{'BJAC'} \hspace{2.5cm} \texttt{'UMF'} \hspace{2.5cm} \texttt{'SLU'}
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\hspace{2.5cm} \texttt{'SLUDIST'}
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& \texttt{'BJAC'}
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& Solver used at the coarsest level: block Jacobi, sequential LU from UMFPACK,
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sequential LU from SuperLU, distributed LU from SuperLU\_Dist.
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If the coarsest matrix is distributed, only \texttt{'BJAC'} and \texttt{'SLUDIST'}
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can be chosen; if it is replicated, only \texttt{'BJAC'} or \texttt{'SLUDIST'} can
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be selected. \\ \hline
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\verb|mld_coarse_subsolve_| & \verb|character(len=*)|
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& \texttt{'ILU'} \hspace{2.5cm} \texttt{'MILU'} \hspace{2.5cm} \texttt{'ILUT'}
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\hspace{2.5cm} \texttt{'UMF'} \hspace{2.5cm} \texttt{'SLU'}
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& \texttt{'UMF'}
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& Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver
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is chosen as coarsest-level solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK,
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LU from SuperLU, plus triangular solve. \\ \hline
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\verb|mld_coarse_sweeps_|& \verb|integer|
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& Any~int.~num.~$> 0$
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& \texttt{4}
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& Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver. \\
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\verb|mld_coarse_fillin_| & \verb|integer|
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& Any~int.~num.~$\ge 0$
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& \texttt{0}
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& Fill-in level $p$ of the incomplete LU factorizations. \\ \hline
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\verb|mld_coarse_iluthrs_| & \verb|real(|\emph{kind\_parameter}\verb|)|
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& Any~real.~num.~$\ge 0$
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& \texttt{0.d0} (or \texttt{0.e0})
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& Drop tolerance $t$ in the ILU($p,t$) factorization. \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Parameters defining the coarse-space correction at the coarsest
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level.\label{tab:p_coarse}}
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\end{sidewaystable}
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\clearpage
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\subsection{Subroutine mld\_precbld\label{sec:precbld}}
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\begin{center}
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\verb|mld_precbld(a,desc_a,p,info)|\\
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\end{center}
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\noindent
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This routine builds the preconditioner according to the requirements made by
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the user through the routines \verb|mld_precinit| and \verb|mld_precset|.
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\subsubsection*{Arguments}
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\begin{tabular}{p{1.2cm}p{10.5cm}}
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\verb|a| & \verb|type(psb_|\emph{x}\verb|spmat_type), intent(in)|. \\
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& The sparse matrix structure containing the local part of the
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matrix to be preconditioned. Note that \emph{x} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.
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See the PSBLAS User's Guide for details \cite{PSBLASGUIDE}.\\
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\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
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& The communication descriptor of \verb|a|. See the PSBLAS User's Guide for
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details \cite{PSBLASGUIDE}.\\
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\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
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& The preconditioner data structure. Note that \emph{x} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.\\
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\verb|info| & \verb|integer, intent(out)|.\\
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& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
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\end{tabular}
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\clearpage
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\subsection{Subroutine mld\_precaply\label{sec:precaply}}
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\begin{center}
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\verb|mld_precaply(p,x,y,desc_a,info)|\\
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\verb|mld_precaply(p,x,y,desc_a,info,trans,work)|\\
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\end{center}
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\noindent
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This routine computes $y = op(M^{-1})\, x$, where $M$ is a previously built
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preconditioner, stored into \verb|p|, and $op$
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denotes the preconditioner itself or its transpose, according to
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the value of \verb|trans|.
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Note that, when MLD2P4 is used with a Krylov solver from PSBLAS,
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\verb|mld_precaply| is called within the PSBLAS routine \verb|mld_krylov|
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and hence it is completely transparent to the user.
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\subsubsection*{Arguments}
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\begin{tabular}{p{1.2cm}p{10.5cm}}
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\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
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& The preconditioner data structure, containing the local part of $M$.
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Note that \emph{x} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.\\
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\verb|x| & \emph{type}\verb|(|\emph{kind\_parameter}\verb|), dimension(:), intent(in)|.\\
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& The local part of the vector $x$. Note that \emph{type} and
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\emph{kind\_parameter} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.\\
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\verb|y| & \emph{type}\verb|(|\emph{kind\_parameter}\verb|), dimension(:), intent(out)|.\\
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& The local part of the vector $y$. Note that \emph{type} and
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\emph{kind\_parameter} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.\\
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\verb|desc_a| & \verb|type(psb_desc_type), intent(in)|. \\
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& The communication descriptor associated to the matrix to be
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preconditioned.\\
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\verb|info| & \verb|integer, intent(out)|.\\
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& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
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\verb|trans| & \verb|character(len=1), optional, intent(in).|\\
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& If \verb|trans| = \verb|'N','n'| then $op(M^{-1}) = M^{-1}$;
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if \verb|trans| = \verb|'T','t'| then $op(M^{-1}) = M^{-T}$
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(transpose of $M^{-1})$; if \verb|trans| = \verb|'C','c'| then $op(M^{-1}) = M^{-C}$
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(conjugate transpose of $M^{-1})$.\\
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\verb|work| & \emph{type}\verb|(|\emph{kind\_parameter}\verb|), dimension(:), optional, target|.\\
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& Workspace. Its size should be at
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least \verb|4 * psb_cd_get_local_cols(desc_a)| (see the PSBLAS User's Guide).
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Note that \emph{type} and \emph{kind\_parameter} must be chosen according
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to the real/complex, single/double precision version of MLD2P4 under use.\\
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\end{tabular}
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\subsection{Subroutine mld\_precfree\label{sec:precfree}}
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\begin{center}
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|
\verb|mld_precfree(p,info)|\\
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\end{center}
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\noindent
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This routine deallocates the preconditioner data structure.
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|
\subsubsection*{Arguments}
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|
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\begin{tabular}{p{1.2cm}p{10.5cm}}
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|
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(inout)|.\\
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|
& The preconditioner data structure. Note that \emph{x} must be chosen according
|
|
to the real/complex, single/double precision version of MLD2P4 under use.\\
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|
\verb|info| & \verb|integer, intent(out)|.\\
|
|
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
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|
\end{tabular}
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\subsection{Subroutine mld\_precdescr\label{sec:precdescr}}
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|
|
|
\begin{center}
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|
\verb|mld_precdescr(p,info)|\\
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|
\verb|mld_precdescr(p,info,iout)|\\
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|
\end{center}
|
|
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|
\noindent
|
|
This routine prints a description of the preconditioner
|
|
to the standard output or to a file.
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|
|
|
\subsubsection*{Arguments}
|
|
|
|
\begin{tabular}{p{1.2cm}p{10.6cm}}
|
|
\verb|p| & \verb|type(mld_|\emph{x}\verb|prec_type), intent(in)|.\\
|
|
& The preconditioner data structure. Note that \emph{x} must be chosen according
|
|
to the real/complex, single/double precision version of MLD2P4 under use.\\
|
|
\verb|info| & \verb|integer, intent(out)|.\\
|
|
& Error code. If no error, 0 is returned. See Section~\ref{sec:errors} for details.\\
|
|
\verb|iout| & \verb|integer, intent(in), optional|.\\
|
|
& The id of the file where the preconditioner description
|
|
will be printed; the default is the standard output.\\
|
|
\end{tabular}
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|
%%% Local Variables:
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|
%%% mode: latex
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%%% TeX-master: "userguide"
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%%% End:
|