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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<HTML>
<HEAD>
<TITLE>User Interface</TITLE>
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<TITLE>Getting Started</TITLE>
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<H1><A NAME="SECTION00080000000000000000"></A><A NAME="sec:userinterface"></A>
<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
<BR>
User Interface
Getting Started
</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">The basic user interface of MLD2P4 consists of eight routines. The six
routines <code>init</code>, <code>set</code>,
<code>hierarchy_build</code>, <code>smoothers_build</code>,
<code>bld</code>, and <code>apply</code> encapsulate all the
functionalities for the setup and the application of any multi-level and one-level
preconditioner implemented in the package.
The routine <code>free</code> deallocates the preconditioner data structure, while
<code>descr</code> prints a description of the preconditioner setup by the user.
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We describe the basics for building and applying MLD2P4 one-level and multi-level
(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
HREF="node29.html#PSBLASGUIDE">13</A>].
The following steps are required:
</FONT></FONT></FONT>
<OL>
<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
<code>mld_</code><I>x</I><code>prec_</code> <code>type</code>, where <I>x</I> may be <code>s</code>, <code>d</code>, <code>c</code>
or <code>z</code>, according to the basic data type of the sparse matrix
(<code>s</code> = real single precision; <code>d</code> = real double precision;
<code>c</code> = complex single precision; <code>z</code> = complex double precision).
This data structure is accessed by the user only through the MLD2P4 routines,
following an object-oriented approach.
</LI>
<LI><I>Allocate and initialize the preconditioner data structure, according to
a preconditioner type chosen by the user</I>. This is performed by the routine
<code>init</code>, 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&nbsp;<A HREF="#tab:precinit">1</A>, where the strings used by
<code>init</code> to identify the preconditioner types are also given.
Note that these strings are valid also if uppercase letters are substituted by
corresponding lowercase ones.
</LI>
<LI><I>Modify the selected preconditioner type, by properly setting
preconditioner parameters.</I> This is performed by the routine <code>set</code>.
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 <code>set</code> are given in
Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>; a complete list of all the
preconditioner parameters and their allowed and default values is provided in
Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>, Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
</LI>
<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
is multi-level, then two steps must be performed, as specified next.
<DL COMPACT>
<DT>4.1</DT>
<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
performed by the routine <code>hierarchy_build</code>.
</DD>
<DT>4.2</DT>
<DD><I>Build the preconditioner for a given matrix.</I> This is performed
by the routine <code>smoothers_build</code>.
</DD>
</DL>
If the selected preconditioner is one-level, it is built in a single step,
performed by the routine <code>bld</code>.
</LI>
<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
this step is completely transparent to the user, since <code>aply</code> is called
by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
</LI>
<LI><I>Free the preconditioner data structure</I>. This is performed by
the routine <code>free</code>. This step is complementary to step 1 and should
be performed when the preconditioner is no more used.
</LI>
</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the routines are available as methods of the preconditioner object.
For each routine, the same user interface is overloaded with
respect to the real/ complex case and the single/double precision;
arguments with appropriate data types must be passed to the routine,
i.e.,
</FONT></FONT></FONT>
<UL>
<LI>the sparse matrix data structure, containing the matrix to be
preconditioned, must be of type <code>psb_</code><I>x</I><code>spmat_type</code>
with <I>x</I> = <code>s</code> for real single precision, <I>x</I> = <code>d</code>
for real double precision, <I>x</I> = <code>c</code> for complex single precision,
<I>x</I> = <code>z</code> for complex double precision;
</LI>
<LI>the preconditioner data structure must be of type
<code>mld_</code><I>x</I><code>prec_type</code>, with <I>x</I> =
<code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, according to the sparse
matrix data structure;
</LI>
<LI>the arrays containing the vectors <IMG
WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img15.png"
ALT="$v$"> and <IMG
WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img16.png"
ALT="$w$"> involved in
the preconditioner application <IMG
WIDTH="82" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img17.png"
ALT="$w=B^{-1}v$"> must be of type
<code>psb_</code><I>x</I><code>vect_type</code> with <I>x</I> =
<code>s</code>, <code>d</code>, <code>c</code>, <code>z</code>, in a manner completely
analogous to the sparse matrix type;
</LI>
<LI>real parameters defining the preconditioner must be declared
according to the precision of the sparse matrix and preconditioner
data structures (see Section&nbsp;<A HREF="node17.html#sec:precset">6.2</A>).
</LI>
</UL><FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">
A description of each routine is given in the remainder of this section.
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the previous routines are available as methods of the preconditioner object.
A detailed description of them is given in Section&nbsp;<A HREF="node17.html#sec:userinterface">6</A>.
Examples showing the basic use of MLD2P4 are reported in Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>.
</FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="857"></A>
<TABLE>
<CAPTION><STRONG>Table 1:</STRONG>
Preconditioner types, corresponding strings and default choices.
</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><SMALL>STRING</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT">No preconditioner</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
Krylov solvers with no preconditioner.</TD>
</TR>
<TR><TD ALIGN="LEFT">Diagonal</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'DIAG'</code> or <code>'JACOBI'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Diagonal preconditioner.
For any zero diagonal entry of the matrix to be preconditioned,
the corresponding entry of the preconditioner is set to&nbsp;1.</TD>
</TR>
<TR><TD ALIGN="LEFT">Block Jacobi</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'BJAC'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Block-Jacobi with ILU(0) on the local blocks.</TD>
</TR>
<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'AS'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Restricted Additive Schwarz (RAS),
with overlap&nbsp;1 and ILU(0) on the local blocks.</TD>
</TR>
<TR><TD ALIGN="LEFT">Multilevel</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'ML'</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>V-cycle with one hybrid forward Gauss-Seidel
(GS) sweep as pre-smoother and one hybrid backward
GS sweep as post-smoother, basic smoothed aggregation
as coarsening algorithm, and LU (plus triangular solve)
as coarsest-level solver. See the default values in
Tables&nbsp;<A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>
for further details of the preconditioner.</TD>
</TR>
</TABLE>
</DIV></TD></TR>
</TABLE>
</DIV><P></P>
<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Note that the module <code>mld_prec_mod</code>, containing the definition of the
preconditioner data type and the interfaces to the routines of MLD2P4,
must be used in any program calling such routines.
The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
data types, and <code>psb_krylov_mod</code>, for interfacing with the
Krylov solvers, must be also used (see Section&nbsp;<A HREF="node16.html#sec:examples">5.1</A>).
<BR></FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
usually lead to smaller numbers of preconditioned Krylov
iterations than inexact solvers, when the linear system comes from
a standard discretization of basic scalar elliptic PDE problems. However,
this does not necessarily correspond to the smallest execution time
on parallel computers. </FONT></FONT></FONT>
<P>
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
<BR><HR>
@@ -115,46 +192,32 @@ A description of each routine is given in the remainder of this section.
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html257"
HREF="node16.html">Subroutine init</A>
<LI><A NAME="tex2html258"
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<LI><A NAME="tex2html259"
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<LI><A NAME="tex2html260"
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<LI><A NAME="tex2html261"
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<LI><A NAME="tex2html262"
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<LI><A NAME="tex2html263"
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<LI><A NAME="tex2html264"
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