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docs/src/gettingstarted.tex
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@@ -15,18 +15,18 @@ The following steps are required:
following an object-oriented approach.
\item \emph{Allocate and initialize the preconditioner data structure, according to
a preconditioner type chosen by the user}. This is performed by the routine
\verb|init|, which also sets defaults for each preconditioner
\fortinline|init|, which also sets defaults for each preconditioner
type selected by the user. The preconditioner types and the defaults associated
with them are given in Table~\ref{tab:precinit}, where the strings used by
\verb|init| to identify the preconditioner types are also given.
\fortinline|init| to identify the preconditioner types are also given.
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
\item \emph{Modify the selected preconditioner type, by properly setting
preconditioner parameters.} This is performed by the routine \verb|set|.
preconditioner parameters.} This is performed by the routine \fortinline|set|.
This routine must be called only if the user wants to modify the default values
of the parameters associated with the selected preconditioner type, to obtain a variant
of that preconditioner. Examples of use of \verb|set| are given in
of that preconditioner. Examples of use of \fortinline|set| are given in
Section~\ref{sec:examples}; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section~\ref{sec:userinterface}, Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.
@@ -34,18 +34,18 @@ The following steps are required:
is multilevel, then two steps must be performed, as specified next.
\begin{enumerate}
\item[4.1] \emph{Build the AMG hierarchy for a given matrix.} This is
performed by the routine \verb|hierarchy_build|.
performed by the routine \fortinline|hierarchy_build|.
\item[4.2] \emph{Build the preconditioner for a given matrix.} This is performed
by the routine \verb|smoothers_build|.
by the routine \fortinline|smoothers_build|.
\end{enumerate}
If the selected preconditioner is one-level, it is built in a single step,
performed by the routine \verb|bld|.
performed by the routine \fortinline|bld|.
\item \emph{Apply the preconditioner at each iteration of a Krylov solver.}
This is performed by the method \verb|apply|. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since \verb|apply| is called
by the PSBLAS routine implementing the Krylov solver (\verb|psb_krylov|).
This is performed by the method \fortinline|apply|. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since \fortinline|apply| is called
by the PSBLAS routine implementing the Krylov solver (\fortinline|psb_krylov|).
\item \emph{Free the preconditioner data structure}. This is performed by
the routine \verb|free|. This step is complementary to step 1 and should
the routine \fortinline|free|. This step is complementary to step 1 and should
be performed when the preconditioner is no more used.
\end{enumerate}
@@ -88,11 +88,11 @@ Multilevel &\fortinline|'ML'| & V-cycle with one hybrid forward Gauss-
\end{center}
\end{table}
Note that the module \verb|amg_prec_mod|, containing the definition of the
Note that the module \fortinline|amg_prec_mod|, containing the definition of the
preconditioner data type and the interfaces to the routines of AMG4PSBLAS,
must be used in any program calling such routines.
The modules \verb|psb_base_mod|, for the sparse matrix and communication descriptor
data types, and \verb|psb_krylov_mod|, for interfacing with the
The modules \fortinline|psb_base_mod|, for the sparse matrix and communication descriptor
data types, and \fortinline|psb_krylov_mod|, for interfacing with the
Krylov solvers, must be also used (see Section~\ref{sec:examples}). \\
\textbf{Remark 1.} Coarsest-level solvers based on the LU factorization,
@@ -109,11 +109,11 @@ on parallel computers.
The code reported in Figure~\ref{fig:ex1} shows how to set and apply the default
multilevel preconditioner available in the real double precision version
of AMG4PSBLAS (see Table~\ref{tab:precinit}). This preconditioner is chosen
by simply specifying \verb|'ML'| as the second argument of \verb|P%init|
(a call to \verb|P%set| is not needed) and is applied with the CG
by simply specifying \fortinline|'ML'| as the second argument of \fortinline|P%init|
(a call to \fortinline|P%set| is not needed) and is applied with the CG
solver provided by PSBLAS (the matrix of the system to be solved is
assumed to be positive definite). As previously observed, the modules
\verb|psb_base_mod|, \verb|amg_prec_mod| and \verb|psb_krylov_mod|
\fortinline|psb_base_mod|, \fortinline|amg_prec_mod| and \fortinline|psb_krylov_mod|
must be used by the example program.
The part of the code concerning the
@@ -134,9 +134,64 @@ precision, versions are obtained with straightforward modifications of the previ
example (see Section~\ref{sec:userinterface} for details). If these versions are installed,
the corresponding codes are available in \verb|examples/fileread/|.
\begin{figure}[tbp]
\begin{listing}[tbp]
\begin{center}
\begin{minipage}{.90\textwidth}
\ifpdf
\begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran}
use psb_base_mod
use amg_prec_mod
use psb_krylov_mod
... ...
!
! sparse matrix
type(psb_dspmat_type) :: A
! sparse matrix descriptor
type(psb_desc_type) :: desc_A
! preconditioner
type(amg_dprec_type) :: P
! right-hand side and solution vectors
type(psb_d_vect_type) :: b, x
... ...
!
! initialize the parallel environment
call psb_init(ctxt)
call psb_info(ctxt,iam,np)
... ...
!
! read and assemble the spd matrix A and the right-hand side b
! using PSBLAS routines for sparse matrix / vector management
... ...
!
! initialize the default multilevel preconditioner, i.e. V-cycle
! with basic smoothed aggregation, 1 hybrid forward/backward
! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
! solver
call P%init('ML',info)
!
! build the preconditioner
call P%hierarchy_build(A,desc_A,info)
call P%smoothers_build(A,desc_A,info)
!
! set the solver parameters and the initial guess
... ...
!
! solve Ax=b with preconditioned CG
call psb_krylov('CG',A,P,b,x,tol,desc_A,info)
... ...
!
! deallocate the preconditioner
call P%free(info)
!
! deallocate other data structures
... ...
!
! exit the parallel environment
call psb_exit(ctxt)
stop
\end{minted}
\else
{\small
\begin{verbatim}
use psb_base_mod
@@ -155,8 +210,8 @@ the corresponding codes are available in \verb|examples/fileread/|.
... ...
!
! initialize the parallel environment
call psb_init(ictxt)
call psb_info(ictxt,iam,np)
call psb_init(ctxt)
call psb_info(ctxt,iam,np)
... ...
!
! read and assemble the spd matrix A and the right-hand side b
@@ -188,15 +243,16 @@ the corresponding codes are available in \verb|examples/fileread/|.
... ...
!
! exit the parallel environment
call psb_exit(ictxt)
call psb_exit(ctxt)
stop
\end{verbatim}
}
\fi
\end{minipage}
\caption{setup and application of the default multilevel preconditioner (example 1).
\label{fig:ex1}}
\end{center}
\end{figure}
\end{listing}
Different versions of the multilevel preconditioner can be obtained by changing
the default values of the preconditioner parameters. The code reported in
@@ -205,7 +261,7 @@ which applies 1 block-Jacobi sweep as pre- and post-smoother,
and solves the coarsest-level system with 8 block-Jacobi sweeps.
Note that the ILU(0) factorization (plus triangular solve) is used as
local solver for the block-Jacobi sweeps, since this is the default associated
with block-Jacobi and set by~\verb|P%init|.
with block-Jacobi and set by~\fortinline|P%init|.
Furthermore, specifying block-Jacobi as coarsest-level
solver implies that the coarsest-level matrix is distributed
among the processes.
@@ -216,7 +272,7 @@ implemented in MUMPS. It is specified that the coarsest-level
matrix is distributed, since MUMPS can be used on both
replicated and distributed matrices, and by default
it is used on replicated ones.
%Note the use of the parameter \verb|pos|
%Note the use of the parameter \fortinline|pos|
%to specify a property only for the pre-smoother or the post-smoother
%(see Section~\ref{sec:precset} for more details).
The code fragments shown in Figures~\ref{fig:ex2} and \ref{fig:ex3} are
@@ -232,8 +288,20 @@ The corresponding example program is available in the file
For all the previous preconditioners, example programs where the sparse matrix and
the right-hand side are generated by discretizing a PDE with Dirichlet
boundary conditions are also available in the directory \verb|examples/pdegen|.
\begin{figure}[tbh]
\vspace{-1em}\begin{listing}[tbh]
\ifpdf%
\begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran}
! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
! ILU(0) on the blocks) as pre- and post-smoother, and 8 block-Jacobi
! sweeps (with ILU(0) on the blocks) as coarsest-level solver
call P%init('ML',info)
call P%set('SMOOTHER_TYPE','BJAC',info)
call P%set('COARSE_SOLVE','BJAC',info)
call P%set('COARSE_SWEEPS',8,info)
call P%hierarchy_build(A,desc_A,info)
call P%smoothers_build(A,desc_A,info)
\end{minted}
\else%
\begin{center}
\begin{minipage}{.90\textwidth}
{\small
@@ -243,7 +311,7 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
! ILU(0) on the blocks) as pre- and post-smoother, and 8 block-Jacobi
! sweeps (with ILU(0) on the blocks) as coarsest-level solver
call P%init('ML',info)
call_P%set('SMOOTHER_TYPE','BJAC',info)
call P%set('SMOOTHER_TYPE','BJAC',info)
call P%set('COARSE_SOLVE','BJAC',info)
call P%set('COARSE_SWEEPS',8,info)
call P%hierarchy_build(A,desc_A,info)
@@ -252,12 +320,27 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
\end{verbatim}
}
\end{minipage}
\caption{setup of a multilevel preconditioner based on the default decoupled coarsening\label{fig:ex2}}
\end{center}
\end{figure}
\begin{figure}[h!]
\fi\vspace{-2em}%
\caption{setup of a multilevel preconditioner based on the default decoupled coarsening\label{fig:ex2}}
\end{listing}\vspace*{-2em}
\begin{listing}[h!]
\ifpdf
\begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran}
! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
! as pre- and post-smoother, a distributed coarsest
! matrix, and MUMPS as coarsest-level solver
call P%init('ML',info)
call P%set('PAR_AGGR_ALG','COUPLED',info)
call P%set('ML_CYCLE','WCYCLE',info)
call P%set('SMOOTHER_TYPE','FBGS',info)
call P%set('SMOOTHER_SWEEPS',2,info)
call P%set('COARSE_SOLVE','MUMPS',info)
call P%set('COARSE_MAT','DIST',info)
call P%hierarchy_build(A,desc_A,info)
call P%smoothers_build(A,desc_A,info)
\end{minted}
\else
\begin{center}
\begin{minipage}{.90\textwidth}
{\small
@@ -279,11 +362,27 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
\end{verbatim}
}
\end{minipage}
\caption{setup of a multilevel preconditioner based on the coupled coarsening based on weighted matching\label{fig:ex3}}
\end{center}
\end{figure}
\begin{figure}[h!]
\fi\vspace{-2em}%
\caption{setup of a multilevel preconditioner based on the coupled coarsening based on weighted matching\label{fig:ex3}}
\end{listing}\vspace*{-2em}
\begin{listing}[h!]
\ifpdf
\begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran}
! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
! as pre- and post-smoother, a distributed coarsest
! matrix, and MUMPS as coarsest-level solver
call P%init('ML',info)
call P%set('PAR_AGGR_ALG','COUPLED',info)
call P%set('ML_CYCLE','WCYCLE',info)
call P%set('SMOOTHER_TYPE','FBGS',info)
call P%set('SMOOTHER_SWEEPS',2,info)
call P%set('COARSE_SOLVE','MUMPS',info)
call P%set('COARSE_MAT','DIST',info)
call P%hierarchy_build(A,desc_A,info)
call P%smoothers_build(A,desc_A,info)
\end{minted}
\else
\begin{center}
\begin{minipage}{.90\textwidth}
{\small
@@ -299,9 +398,10 @@ boundary conditions are also available in the directory \verb|examples/pdegen|.
\end{verbatim}
}
\end{minipage}
\caption{setup of a one-level Schwarz preconditioner.\label{fig:ex4}}
\end{center}
\end{figure}
\fi\vspace{-2em}%
\caption{setup of a one-level Schwarz preconditioner.\label{fig:ex4}}
\end{listing}
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