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\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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Preconditioning is somehow regarded as ``black magic''. This is due to
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the fact that theory doesn't provide a reliable support in the choice
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of a preconditioner. It is clear that the influence of a
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preconditioning technique on the convergence behavior of an iterative
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method mostly depends on the characteristics of the system matrix and
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of the method itself. Anyway it is not possible a priori to say that
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one preconditioner is algebrically better than another and this perfectly explains
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the importance of providing a wide range of preconditioners techniques
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so that the user can find by itself which one is more suitable for his
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problem. Moreover, there are some other issues to consider when
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choosing a preconditioner such as balancing the overhead of building
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the preconditioner with the reduction in the number of
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iterations. PSBLAS contains the implementation of many preconditioning
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techniques some of which are very flexible thanks to the presence of
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many parameters that is possible to adjust to fit the user's needs:
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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 (see
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chapter~\ref{sec:pprec})
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\item Two-Level Additive Schwarz; 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 as explained in chapter~\ref{sec:mlprec}
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\end{itemize}
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\subroutine{psb\_precset}{Sets the precodntioner type}
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\syntax{call psb\_precset}{prec, ptype, iv, rs, rv, ierr}
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\begin{description}
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\item[\bf On Entry]
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\item[prec]
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Specified as: e pronditioner data structure \precdata.
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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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Specified as: a string.
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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.
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\item[rs]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\item[rv]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\item[ierr]
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Scope: {\bf } \\
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Type: {\bf }\\
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Specified as: .
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\end{description}
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\subroutine{psb\_precbld}{Builds a preconditioner}
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\syntax{call psb\_precbld}{a, desc\_a, prec, info, upd}
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\begin{description}
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\item[\bf On Entry]
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\item[a] the system sparse matrix.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Specified as: a sparse matrix data structure \spdata.
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\item[desc\_a] the problem communication descriptor.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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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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Specified as: a character.
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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 precodntioner.\\
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Specified as: a precondtioner data structure \precdata\\
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\item[info] the return error code.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: an integer.\\
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\end{description}
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\subroutine{psb\_precaply}{Preconditioner application routine}
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\syntax{call psb\_precaply}{prec,x,y,desc\_a,info,trans,work}
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\syntax{call psb\_precaply}{prec,x,desc\_a,info,trans}
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\begin{description}
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\item[\bf On Entry]
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\item[prec] the preconditioner.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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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 global} \\
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Type: {\bf require}\\
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Specified as: a double precision array.
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\item[desc\_a] the problem communication descriptor.
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Scope: {\bf global} \\
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Type: {\bf required}\\
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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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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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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 global} \\
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Type: {\bf required}\\
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Specified as: a double precision array.
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\item[info] the return error code.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: an integer.\\
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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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