|
|
|
|
\section{Preconditioner routines}
|
|
|
|
|
\label{sec:precs}
|
|
|
|
|
|
|
|
|
|
% \section{Preconditioners}
|
|
|
|
|
\label{sec:psprecs}
|
|
|
|
|
The base PSBLAS library contains the implementation of two simple
|
|
|
|
|
preconditioning techniques:
|
|
|
|
|
\begin{itemize}
|
|
|
|
|
\item Diagonal Scaling
|
|
|
|
|
\item Block Jacobi with ILU(0) factorization
|
|
|
|
|
%% \item Additive Schwarz with the Restricted Additive Schwarz and
|
|
|
|
|
%% Additive Schwarz with Harmonic extensions;
|
|
|
|
|
\end{itemize}
|
|
|
|
|
The supporting data type and subroutine interfaces are defined in the
|
|
|
|
|
module \verb|psb_prec_mod|.
|
|
|
|
|
|
|
|
|
|
%% We also provide a companion package of multi-level Additive
|
|
|
|
|
%% Schwarz preconditioners called MD2P4; this is actually a family of
|
|
|
|
|
%% preconditioners since there is the possibility to choose between
|
|
|
|
|
%% many variants, and is currently in an experimental stateIts
|
|
|
|
|
%% documentation is planned to appear after stabilization of the
|
|
|
|
|
%% package, which will characterize release 2.1 of our library.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\clearpage\subsection*{psb\_precinit --- Initialize a preconditioner}
|
|
|
|
|
\addcontentsline{toc}{subsection}{psb\_precinit}
|
|
|
|
|
|
|
|
|
|
\begin{verbatim}
|
|
|
|
|
call psb_precinit(prec, ptype, info)
|
|
|
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[Type:] Asynchronous.
|
|
|
|
|
\item[\bf On Entry]
|
|
|
|
|
\item[ptype] the type of preconditioner.
|
|
|
|
|
Scope: {\bf global} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: a character string, see usage notes.
|
|
|
|
|
%% \item[iv] integer parameters for the precondtioner.
|
|
|
|
|
%% Scope: {\bf global} \\
|
|
|
|
|
%% Type: {\bf required}\\
|
|
|
|
|
%% Specified as: an integer array, see usage notes.
|
|
|
|
|
%% \item[rs]
|
|
|
|
|
%% Scope: {\bf global} \\
|
|
|
|
|
%% Type: {\bf optional}\\
|
|
|
|
|
%% Specified as: a long precision real number.
|
|
|
|
|
\item[\bf On Exit]
|
|
|
|
|
|
|
|
|
|
\item[prec]
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: a preconditioner data structure \precdata.
|
|
|
|
|
\item[info]
|
|
|
|
|
Scope: {\bf global} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf out}.\\
|
|
|
|
|
Error code: if no error, 0 is returned.
|
|
|
|
|
\end{description}
|
|
|
|
|
{\par\noindent\large\bfseries Notes}
|
|
|
|
|
%% The PSBLAS 2.0 contains a number of preconditioners, ranging from a
|
|
|
|
|
%% simple diagonal scaling to 2-level domain decomposition. These
|
|
|
|
|
%% preconditioners may use the SuperLU or the UMFPACK software, if
|
|
|
|
|
%% installed; see~\cite{SUPERLU,UMFPACK}.
|
|
|
|
|
Legal inputs to this subroutine are interpreted depending on the
|
|
|
|
|
$ptype$ string as follows\footnote{The string is case-insensitive}:
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[NONE] No preconditioning, i.e. the preconditioner is just a copy
|
|
|
|
|
operator.
|
|
|
|
|
\item[DIAG] Diagonal scaling; each entry of the input vector is
|
|
|
|
|
multiplied by the reciprocal of the sum of the absolute values of
|
|
|
|
|
the coefficients in the corresponding row of matrix $A$;
|
|
|
|
|
\item[BJAC] Precondition by a factorization of the
|
|
|
|
|
block-diagonal of matrix $A$, where block boundaries are determined
|
|
|
|
|
by the data allocation boundaries for each process; requires no
|
|
|
|
|
communication. Only the incomplete factorization $ILU(0)$ is
|
|
|
|
|
currently implemented.
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\clearpage\subsection*{psb\_precbld --- Builds a preconditioner}
|
|
|
|
|
\addcontentsline{toc}{subsection}{psb\_precbld}
|
|
|
|
|
|
|
|
|
|
\begin{verbatim}
|
|
|
|
|
call psb_precbld(a, desc_a, prec, info,amold,vmold)
|
|
|
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[Type:] Synchronous.
|
|
|
|
|
\item[\bf On Entry]
|
|
|
|
|
\item[a] the system sparse matrix.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}, target.\\
|
|
|
|
|
Specified as: a sparse matrix data structure \spdata.
|
|
|
|
|
\item[prec] the preconditioner.\\
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: an already initialized precondtioner data structure \precdata\\
|
|
|
|
|
\item[desc\_a] the problem communication descriptor.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}, target.\\
|
|
|
|
|
Specified as: a communication descriptor data structure \descdata.
|
|
|
|
|
%% \item[upd]
|
|
|
|
|
%% Scope: {\bf global} \\
|
|
|
|
|
%% Type: {\bf optional}\\
|
|
|
|
|
%% Intent: {\bf in}.\\
|
|
|
|
|
%% Specified as: a character.
|
|
|
|
|
\item[amold] The desired dynamic type for the internal matrix storage.\\
|
|
|
|
|
Scope: {\bf local}.\\
|
|
|
|
|
Type: {\bf optional}.\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: an object of a class derived from \spbasedata.
|
|
|
|
|
\item[vmold] The desired dynamic type for the internal vector storage.\\
|
|
|
|
|
Scope: {\bf local}.\\
|
|
|
|
|
Type: {\bf optional}.\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: an object of a class derived from \vbasedata.
|
|
|
|
|
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[\bf On Return]
|
|
|
|
|
\item[prec] the preconditioner.\\
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: a precondtioner data structure \precdata\\
|
|
|
|
|
\item[info] Error code.\\
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required} \\
|
|
|
|
|
Intent: {\bf out}.\\
|
|
|
|
|
An integer value; 0 means no error has been detected.
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\clearpage\subsection*{psb\_precaply --- Preconditioner application routine}
|
|
|
|
|
\addcontentsline{toc}{subsection}{psb\_precaply}
|
|
|
|
|
|
|
|
|
|
\begin{verbatim}
|
|
|
|
|
call psb_precaply(prec,x,y,desc_a,info,trans,work)
|
|
|
|
|
call psb_precaply(prec,x,desc_a,info,trans)
|
|
|
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[Type:] Synchronous.
|
|
|
|
|
\item[\bf On Entry]
|
|
|
|
|
\item[prec] the preconditioner.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: a preconditioner data structure \precdata.
|
|
|
|
|
\item[x] the source vector.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: a rank one array or an object of type \vdata.
|
|
|
|
|
\item[desc\_a] the problem communication descriptor.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: a communication data structure \descdata.
|
|
|
|
|
\item[trans]
|
|
|
|
|
Scope: {\bf } \\
|
|
|
|
|
Type: {\bf optional}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: a character.
|
|
|
|
|
\item[work] an optional work space
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf optional}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: a double precision array.
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[\bf On Return]
|
|
|
|
|
\item[y] the destination vector.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf inout}.\\
|
|
|
|
|
Specified as: a rank one array or an object of type \vdata.
|
|
|
|
|
\item[info] Error code.\\
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required} \\
|
|
|
|
|
Intent: {\bf out}.\\
|
|
|
|
|
An integer value; 0 means no error has been detected.
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\clearpage\subsection*{psb\_precdescr --- Prints a description of current
|
|
|
|
|
preconditioner}
|
|
|
|
|
\addcontentsline{toc}{subsection}{psb\_precdescr}
|
|
|
|
|
|
|
|
|
|
\begin{verbatim}
|
|
|
|
|
call psb_precdescr(prec)
|
|
|
|
|
call psb_precdescr(prec, iout)
|
|
|
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
\begin{description}
|
|
|
|
|
\item[Type:] Asynchronous.
|
|
|
|
|
\item[\bf On Entry]
|
|
|
|
|
\item[prec] the preconditioner.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf required}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: a preconditioner data structure \precdata.
|
|
|
|
|
\item[iout] output unit.
|
|
|
|
|
Scope: {\bf local} \\
|
|
|
|
|
Type: {\bf optiona}\\
|
|
|
|
|
Intent: {\bf in}.\\
|
|
|
|
|
Specified as: an integer number.
|
|
|
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
|
|
|
%%% mode: latex
|
|
|
|
|
%%% TeX-master: "userguide"
|
|
|
|
|
%%% End:
|
