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