psblas3:
docs/html/footnode.html docs/html/img152.png docs/html/img154.png docs/html/img155.png docs/html/img156.png docs/html/img157.png docs/html/img158.png docs/html/img159.png docs/html/img160.png docs/html/img161.png docs/html/img162.png docs/html/img163.png docs/html/img164.png docs/html/img165.png docs/html/img166.png docs/html/index.html docs/html/node1.html docs/html/node10.html docs/html/node100.html docs/html/node101.html docs/html/node102.html docs/html/node103.html docs/html/node104.html docs/html/node105.html docs/html/node106.html docs/html/node107.html docs/html/node108.html docs/html/node109.html docs/html/node11.html docs/html/node110.html docs/html/node111.html docs/html/node112.html docs/html/node113.html docs/html/node114.html docs/html/node115.html docs/html/node116.html docs/html/node117.html docs/html/node118.html docs/html/node119.html docs/html/node12.html docs/html/node120.html docs/html/node121.html docs/html/node122.html docs/html/node123.html docs/html/node124.html docs/html/node125.html docs/html/node126.html docs/html/node127.html docs/html/node128.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node32.html docs/html/node33.html docs/html/node34.html docs/html/node35.html docs/html/node36.html docs/html/node37.html docs/html/node38.html docs/html/node39.html docs/html/node4.html docs/html/node40.html docs/html/node41.html docs/html/node42.html docs/html/node43.html docs/html/node44.html docs/html/node45.html docs/html/node46.html docs/html/node47.html docs/html/node48.html docs/html/node49.html docs/html/node5.html docs/html/node50.html docs/html/node51.html docs/html/node52.html docs/html/node53.html docs/html/node54.html docs/html/node55.html docs/html/node56.html docs/html/node57.html docs/html/node58.html docs/html/node59.html docs/html/node6.html docs/html/node60.html docs/html/node61.html docs/html/node62.html docs/html/node63.html docs/html/node64.html docs/html/node65.html docs/html/node66.html docs/html/node67.html docs/html/node68.html docs/html/node69.html docs/html/node7.html docs/html/node70.html docs/html/node71.html docs/html/node72.html docs/html/node73.html docs/html/node74.html docs/html/node75.html docs/html/node76.html docs/html/node77.html docs/html/node78.html docs/html/node79.html docs/html/node8.html docs/html/node80.html docs/html/node81.html docs/html/node82.html docs/html/node83.html docs/html/node84.html docs/html/node85.html docs/html/node86.html docs/html/node87.html docs/html/node88.html docs/html/node89.html docs/html/node9.html docs/html/node90.html docs/html/node91.html docs/html/node92.html docs/html/node93.html docs/html/node94.html docs/html/node95.html docs/html/node96.html docs/html/node97.html docs/html/node98.html docs/html/node99.html docs/html/userhtml.html docs/psblas-3.2.pdf docs/src/util.tex util/psb_c_mmio_impl.f90 util/psb_d_mmio_impl.f90 util/psb_mmio_mod.f90 util/psb_s_mmio_impl.f90 util/psb_z_mmio_impl.f90 New interface for mm_array_read/write and docs update.psblas-3.2.0
Salvatore Filippone
12 years ago
parent
9f99a6f782
commit
1609ab9ffe
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<TITLE>clone -- clone current preconditioner</TITLE>
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<BR>
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<B> Next:</B> <A NAME="tex2html1791"
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HREF="node125.html">Iterative Methods</A>
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<B> Up:</B> <A NAME="tex2html1787"
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HREF="node119.html">Preconditioner routines</A>
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<B> Previous:</B> <A NAME="tex2html1783"
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HREF="node123.html">psb_precdescr Prints</A>
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<H2><A NAME="SECTION000115000000000000000">
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clone -- clone current
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preconditioner</A>
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</H2>
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<PRE>
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call prec%clone(precout,info)
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</PRE>
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<P>
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<DL>
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<DT><STRONG>Type:</STRONG></DT>
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<DD>Asynchronous.
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</DD>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>prec</STRONG></DT>
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<DD>the preconditioner.
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<BR>
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Scope: <B>local</B>.
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<BR></DD>
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</DL>
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<P>
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<DL>
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<DT><STRONG><B>On Return</B></STRONG></DT>
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<DD>
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</DD>
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<DT><STRONG>precout</STRONG></DT>
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<DD>A copy of the input object.
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</DD>
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<DT><STRONG>info</STRONG></DT>
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<DD>Return code.
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</DD>
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</DL>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2008 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>Iterative Methods</TITLE>
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<META NAME="description" CONTENT="Iterative Methods">
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HREF="node126.html">
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<BR>
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<B> Next:</B> <A NAME="tex2html1803"
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HREF="node126.html">psb_krylov Krylov</A>
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<B> Up:</B> <A NAME="tex2html1799"
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html1793"
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HREF="node124.html">clone clone</A>
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<B> <A NAME="tex2html1801"
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HREF="node1.html">Contents</A></B>
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<H1><A NAME="SECTION000120000000000000000"></A>
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<A NAME="sec:methods"></A>
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<BR>
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Iterative Methods
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</H1>
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<P>
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In this chapter we provide routines for preconditioners and iterative
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methods. The interfaces for Krylov subspace methods are available in
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the module <code>psb_krylov_mod</code>.
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html1804"
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HREF="node126.html">psb_krylov -- Krylov Methods Driver
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Routine</A>
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</UL>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2008 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<TITLE>psb_krylov -- Krylov Methods Driver Routine</TITLE>
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<META NAME="description" CONTENT="psb_krylov -- Krylov Methods Driver Routine">
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<META NAME="Generator" CONTENT="LaTeX2HTML v2008">
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<B> Next:</B> <A NAME="tex2html1814"
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HREF="node127.html">Bibliography</A>
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<B> Up:</B> <A NAME="tex2html1810"
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HREF="node125.html">Iterative Methods</A>
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<B> Previous:</B> <A NAME="tex2html1806"
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HREF="node125.html">Iterative Methods</A>
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<H2><A NAME="SECTION000121000000000000000"></A><A NAME="krylov"></A>
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<BR>
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psb_krylov -- Krylov Methods Driver
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Routine
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</H2>
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<P>
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This subroutine is a driver that provides a general interface for all
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the Krylov-Subspace family methods implemented in PSBLAS version 2.
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<P>
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The stopping criterion is the normwise backward error, in the infinity
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norm, i.e. the iteration is stopped when
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<BR><P></P>
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<DIV ALIGN="CENTER">
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<!-- MATH
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\begin{displaymath}
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err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps
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\end{displaymath}
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ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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or the 2-norm residual reduction
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<!-- MATH
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\begin{displaymath}
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err = \frac{\|r_i\|}{\|b\|_2} < eps
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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according to the value passed through the istop argument (see
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later). In the above formulae, <IMG
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ALT="$x_i$"> is the tentative solution and
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<IMG
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WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||||
|
SRC="img160.png"
|
||||||
|
ALT="$r_i=b-Ax_i$"> the corresponding residual at the <IMG
|
||||||
|
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img4.png"
|
||||||
|
ALT="$i$">-th iteration.
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<BR>
|
||||||
|
<IMG
|
||||||
|
WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img161.png"
|
||||||
|
ALT="\begin{lstlisting}
|
||||||
|
call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
|
||||||
|
& itmax,iter,err,itrace,irst,istop,cond)
|
||||||
|
\end{lstlisting}">
|
||||||
|
<BR>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<DL>
|
||||||
|
<DT><STRONG>Type:</STRONG></DT>
|
||||||
|
<DD>Synchronous.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG><B>On Entry</B></STRONG></DT>
|
||||||
|
<DD>
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>method</STRONG></DT>
|
||||||
|
<DD>a string that defines the iterative method to be
|
||||||
|
used. Supported values are:
|
||||||
|
<DL>
|
||||||
|
<DT><STRONG>CG:</STRONG></DT>
|
||||||
|
<DD>the Conjugate Gradient method;
|
||||||
|
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>CGS:</STRONG></DT>
|
||||||
|
<DD>the Conjugate Gradient Stabilized method;
|
||||||
|
|
||||||
|
<P>
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>BICG:</STRONG></DT>
|
||||||
|
<DD>the Bi-Conjugate Gradient method;
|
||||||
|
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>BICGSTAB:</STRONG></DT>
|
||||||
|
<DD>the Bi-Conjugate Gradient Stabilized method;
|
||||||
|
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>BICGSTABL:</STRONG></DT>
|
||||||
|
<DD>the Bi-Conjugate Gradient Stabilized method with restarting;
|
||||||
|
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>RGMRES:</STRONG></DT>
|
||||||
|
<DD>the Generalized Minimal Residual method with restarting.
|
||||||
|
|
||||||
|
</DD>
|
||||||
|
</DL>
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>a</STRONG></DT>
|
||||||
|
<DD>the local portion of global sparse matrix
|
||||||
|
<IMG
|
||||||
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img1.png"
|
||||||
|
ALT="$A$">.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>prec</STRONG></DT>
|
||||||
|
<DD>The data structure containing the preconditioner.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a structured data of type precdata<TT>psb_prec_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>b</STRONG></DT>
|
||||||
|
<DD>The RHS vector.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>x</STRONG></DT>
|
||||||
|
<DD>The initial guess.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>inout</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>eps</STRONG></DT>
|
||||||
|
<DD>The stopping tolerance.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a real number.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>desc_a</STRONG></DT>
|
||||||
|
<DD>contains data structures for communications.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>itmax</STRONG></DT>
|
||||||
|
<DD>The maximum number of iterations to perform.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Default: <IMG
|
||||||
|
WIDTH="100" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img162.png"
|
||||||
|
ALT="$itmax = 1000$">.
|
||||||
|
<BR>
|
||||||
|
Specified as: an integer variable <IMG
|
||||||
|
WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||||
|
SRC="img163.png"
|
||||||
|
ALT="$itmax \ge 1$">.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>itrace</STRONG></DT>
|
||||||
|
<DD>If <IMG
|
||||||
|
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||||
|
SRC="img112.png"
|
||||||
|
ALT="$>0$"> print out an informational message about
|
||||||
|
convergence every <IMG
|
||||||
|
WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img164.png"
|
||||||
|
ALT="$itrace$"> iterations.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR></DD>
|
||||||
|
<DT><STRONG>irst</STRONG></DT>
|
||||||
|
<DD>An integer specifying the restart parameter.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>.
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Values: <IMG
|
||||||
|
WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
||||||
|
SRC="img165.png"
|
||||||
|
ALT="$irst>0$">. This is employed for the BiCGSTABL or RGMRES
|
||||||
|
methods, otherwise it is ignored.
|
||||||
|
|
||||||
|
<P>
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>istop</STRONG></DT>
|
||||||
|
<DD>An integer specifying the stopping criterion.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>.
|
||||||
|
<BR>
|
||||||
|
Intent: <B>in</B>.
|
||||||
|
<BR>
|
||||||
|
Values: 1: use the normwise backward error, 2: use the scaled 2-norm
|
||||||
|
of the residual. Default: 2.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG><B>On Return</B></STRONG></DT>
|
||||||
|
<DD>
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>x</STRONG></DT>
|
||||||
|
<DD>The computed solution.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>inout</B>.
|
||||||
|
<BR>
|
||||||
|
Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>iter</STRONG></DT>
|
||||||
|
<DD>The number of iterations performed.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>out</B>.
|
||||||
|
<BR>
|
||||||
|
Returned as: an integer variable.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>err</STRONG></DT>
|
||||||
|
<DD>The convergence estimate on exit.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>out</B>.
|
||||||
|
<BR>
|
||||||
|
Returned as: a real number.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>cond</STRONG></DT>
|
||||||
|
<DD>An estimate of the condition number of matrix <IMG
|
||||||
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img1.png"
|
||||||
|
ALT="$A$">; only
|
||||||
|
available with the <IMG
|
||||||
|
WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||||
|
SRC="img166.png"
|
||||||
|
ALT="$CG$"> method.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>global</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>optional</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>out</B>.
|
||||||
|
<BR>
|
||||||
|
Returned as: a real number.
|
||||||
|
</DD>
|
||||||
|
<DT><STRONG>info</STRONG></DT>
|
||||||
|
<DD>Error code.
|
||||||
|
<BR>
|
||||||
|
Scope: <B>local</B>
|
||||||
|
<BR>
|
||||||
|
Type: <B>required</B>
|
||||||
|
<BR>
|
||||||
|
Intent: <B>out</B>.
|
||||||
|
<BR>
|
||||||
|
An integer value; 0 means no error has been detected.
|
||||||
|
</DD>
|
||||||
|
</DL>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
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|
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<H2><A NAME="SECTION000130000000000000000">
|
||||||
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Bibliography</A>
|
||||||
|
</H2><DL COMPACT><DD><P></P><DT><A NAME="DesPat:11">1</A>
|
||||||
|
<DD>
|
||||||
|
D. Barbieri, V. Cardellini, S. Filippone and D. Rouson
|
||||||
|
<EM>Design Patterns for Scientific Computations on Sparse Matrices</EM>,
|
||||||
|
HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<P></P><DT><A NAME="PARA04FOREST">2</A>
|
||||||
|
<DD>
|
||||||
|
G. Bella, S. Filippone, A. De Maio and M. Testa,
|
||||||
|
<EM>A Simulation Model for Forest Fires</EM>,
|
||||||
|
in J. Dongarra, K. Madsen, J. Wasniewski, editors,
|
||||||
|
Proceedings of PARA 04 Workshop on State of the Art
|
||||||
|
in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science,
|
||||||
|
Springer, 2005.
|
||||||
|
<P></P><DT><A NAME="2007d">3</A>
|
||||||
|
<DD> A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,<BR>
|
||||||
|
2LEV-D2P4: a package of high-performance preconditioners,<BR>
|
||||||
|
Applicable Algebra in Engineering, Communications and Computing,
|
||||||
|
Volume 18, Number 3, May, 2007, pp. 223-239
|
||||||
|
<P></P><DT><A NAME="2007c">4</A>
|
||||||
|
<DD> P. D'Ambra, S. Filippone, D. Di Serafino<BR>
|
||||||
|
On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners
|
||||||
|
<BR>
|
||||||
|
Applied Numerical Mathematics, Elsevier Science,
|
||||||
|
Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<P></P><DT><A NAME="BLAS2">5</A>
|
||||||
|
<DD>
|
||||||
|
Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R.,
|
||||||
|
An Extended Set of Fortran Basic Linear Algebra Subprograms,
|
||||||
|
ACM Trans. Math. Softw. vol. 14, 1-17, 1988.
|
||||||
|
<P></P><DT><A NAME="BLAS3">6</A>
|
||||||
|
<DD>
|
||||||
|
Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I.,
|
||||||
|
A Set of level 3 Basic Linear Algebra Subprograms,
|
||||||
|
ACM Trans. Math. Softw. vol. 16, 1-17, 1990.
|
||||||
|
<P></P><DT><A NAME="BLACS">7</A>
|
||||||
|
<DD>
|
||||||
|
J. J. Dongarra and R. C. Whaley,
|
||||||
|
<EM>A User's Guide to the BLACS v. 1.1</EM>,
|
||||||
|
Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of
|
||||||
|
Tennessee, March 1995 (updated May 1997).
|
||||||
|
<P></P><DT><A NAME="sblas97">8</A>
|
||||||
|
<DD>
|
||||||
|
I. Duff, M. Marrone, G. Radicati and C. Vittoli,
|
||||||
|
<EM>Level 3 Basic Linear Algebra Subprograms for Sparse Matrices:
|
||||||
|
a User Level Interface</EM>,
|
||||||
|
ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997.
|
||||||
|
<P></P><DT><A NAME="sblas02">9</A>
|
||||||
|
<DD>
|
||||||
|
I. Duff, M. Heroux and R. Pozo,
|
||||||
|
<EM>An Overview of the Sparse Basic Linear
|
||||||
|
Algebra Subprograms: the New Standard from the BLAS Technical Forum</EM>,
|
||||||
|
ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002.
|
||||||
|
<P></P><DT><A NAME="PSBLAS">10</A>
|
||||||
|
<DD>
|
||||||
|
S. Filippone and M. Colajanni,
|
||||||
|
<EM>PSBLAS: A Library for Parallel Linear Algebra
|
||||||
|
Computation on Sparse Matrices</EM>,
|
||||||
|
<BR>
|
||||||
|
ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000.
|
||||||
|
<P></P><DT><A NAME="Sparse03">11</A>
|
||||||
|
<DD>
|
||||||
|
S. Filippone and A. Buttari,
|
||||||
|
<EM>Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003</EM>,
|
||||||
|
<BR>
|
||||||
|
ACM Transactions on Mathematical Software, to appear.
|
||||||
|
<P></P><DT><A NAME="KIVA3PSBLAS">12</A>
|
||||||
|
<DD>
|
||||||
|
S. Filippone, P. D'Ambra, M. Colajanni,
|
||||||
|
<EM>Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics
|
||||||
|
Applications Code on Linux Clusters</EM>,
|
||||||
|
in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors,
|
||||||
|
Parallel Computing - Advances & Current Issues,
|
||||||
|
pp. 441-448, Imperial College Press, 2002.
|
||||||
|
<P></P><DT><A NAME="DesignPatterns">13</A>
|
||||||
|
<DD>
|
||||||
|
Gamma, E., Helm, R., Johnson, R., and Vlissides,
|
||||||
|
J. 1995.
|
||||||
|
<EM>Design Patterns: Elements of Reusable Object-Oriented Software</EM>.
|
||||||
|
Addison-Wesley.
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<P></P><DT><A NAME="METIS">14</A>
|
||||||
|
<DD>
|
||||||
|
Karypis, G. and Kumar, V.,
|
||||||
|
<EM>METIS: Unstructured Graph Partitioning and Sparse Matrix
|
||||||
|
Ordering System</EM>.
|
||||||
|
Minneapolis, MN 55455: University of Minnesota, Department of
|
||||||
|
Computer Science, 1995.
|
||||||
|
Internet Address: <code>http://www.cs.umn.edu/~karypis</code>.
|
||||||
|
<P></P><DT><A NAME="BLAS1">15</A>
|
||||||
|
<DD>
|
||||||
|
Lawson, C., Hanson, R., Kincaid, D. and Krogh, F.,
|
||||||
|
Basic Linear Algebra Subprograms for Fortran usage,
|
||||||
|
ACM Trans. Math. Softw. vol. 5, 38-329, 1979.
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<P></P><DT><A NAME="machiels">16</A>
|
||||||
|
<DD>
|
||||||
|
Machiels, L. and Deville, M.
|
||||||
|
<EM>Fortran 90: An entry to object-oriented programming for the solution
|
||||||
|
of partial differential equations.</EM>
|
||||||
|
ACM Trans. Math. Softw. vol. 23, 32-49.
|
||||||
|
<P></P><DT><A NAME="metcalf">17</A>
|
||||||
|
<DD>
|
||||||
|
Metcalf, M., Reid, J. and Cohen, M.
|
||||||
|
<EM>Fortran 95/2003 explained.</EM>
|
||||||
|
Oxford University Press, 2004.
|
||||||
|
<P></P><DT><A NAME="RouXiaXu:11">18</A>
|
||||||
|
<DD>
|
||||||
|
Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The
|
||||||
|
Object-Oriented Way. Cambridge University Press (2011)
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<P></P><DT><A NAME="MPI1">19</A>
|
||||||
|
<DD>
|
||||||
|
M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra,
|
||||||
|
<EM>MPI: The Complete Reference. Volume 1 - The MPI Core</EM>, second edition,
|
||||||
|
MIT Press, 1998.
|
||||||
|
</DL>
|
||||||
|
|
||||||
|
<P>
|
||||||
|
<BR><HR>
|
||||||
|
|
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|
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|
||||||
|
</HTML>
|
||||||
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<!--Converted with LaTeX2HTML 2008 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
|
||||||
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||||||
|
* with significant contributions from:
|
||||||
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
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|
<HTML>
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|
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|
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|
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<P>
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This document was generated using the
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Copyright © 1993, 1994, 1995, 1996,
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Computer Based Learning Unit, University of Leeds.
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Copyright © 1997, 1998, 1999,
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