<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 2002-2-1 (1.71) original version by: Nikos Drakos, CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>psb_krylov -- Krylov Methods Driver Routine</TITLE> <META NAME="description" CONTENT="psb_krylov -- Krylov Methods Driver Routine"> <META NAME="keywords" CONTENT="userhtml"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1"> <META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css"> <LINK REL="STYLESHEET" HREF="userhtml.css"> <LINK REL="previous" HREF="node116.html"> <LINK REL="up" HREF="node116.html"> <LINK REL="next" HREF="node118.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html1594" HREF="node118.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="file:/usr/share/latex2html/icons/next.png"></A> <A NAME="tex2html1590" HREF="node116.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="file:/usr/share/latex2html/icons/up.png"></A> <A NAME="tex2html1586" HREF="node116.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="file:/usr/share/latex2html/icons/prev.png"></A> <A NAME="tex2html1592" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="file:/usr/share/latex2html/icons/contents.png"></A> <BR> <B> Next:</B> <A NAME="tex2html1595" HREF="node118.html">Bibliography</A> <B> Up:</B> <A NAME="tex2html1591" HREF="node116.html">Iterative Methods</A> <B> Previous:</B> <A NAME="tex2html1587" HREF="node116.html">Iterative Methods</A> <B> <A NAME="tex2html1593" HREF="node1.html">Contents</A></B> <BR> <BR> <!--End of Navigation Panel--> <H2><A NAME="SECTION000521000000000000000"></A><A NAME="krylov"></A> <BR> psb_krylov -- Krylov Methods Driver Routine </H2> <P> This subroutine is a driver that provides a general interface for all the Krylov-Subspace family methods implemented in PSBLAS version 2. <P> The stopping criterion is the normwise backward error, in the infinity norm, i.e. the iteration is stopped when <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH \begin{displaymath} err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps \end{displaymath} --> <IMG WIDTH="204" HEIGHT="44" BORDER="0" SRC="img137.png" ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath}"> </DIV> <BR CLEAR="ALL"> <P></P> or the 2-norm residual reduction <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH \begin{displaymath} err = \frac{\|r_i\|}{\|b\|_2} < eps \end{displaymath} --> <IMG WIDTH="121" HEIGHT="44" BORDER="0" SRC="img138.png" ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath}"> </DIV> <BR CLEAR="ALL"> <P></P> according to the value passed through the istop argument (see later). In the above formulae, <IMG WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" SRC="img139.png" ALT="$x_i$"> is the tentative solution and <IMG WIDTH="90" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" SRC="img140.png" ALT="$r_i=b-Ax_i$"> the corresponding residual at the <IMG WIDTH="10" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" SRC="img3.png" ALT="$i$">-th iteration. <P> ifstarssyntaxsyntaxcall psb_krylovmethod,a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,istop,cond <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_spmat_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. </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. </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="img141.png" ALT="$itmax = 1000$">. <BR> Specified as: an integer variable <IMG WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img142.png" ALT="$itmax \ge 1$">. </DD> <DT><STRONG>itrace</STRONG></DT> <DD>If <IMG WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" SRC="img103.png" ALT="$>0$"> print out an informational message about convergence every <IMG WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" SRC="img143.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="59" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img144.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. </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="img145.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> <HR> <!--Navigation Panel--> <A NAME="tex2html1594" HREF="node118.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="file:/usr/share/latex2html/icons/next.png"></A> <A NAME="tex2html1590" HREF="node116.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="file:/usr/share/latex2html/icons/up.png"></A> <A NAME="tex2html1586" HREF="node116.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="file:/usr/share/latex2html/icons/prev.png"></A> <A NAME="tex2html1592" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="file:/usr/share/latex2html/icons/contents.png"></A> <BR> <B> Next:</B> <A NAME="tex2html1595" HREF="node118.html">Bibliography</A> <B> Up:</B> <A NAME="tex2html1591" HREF="node116.html">Iterative Methods</A> <B> Previous:</B> <A NAME="tex2html1587" HREF="node116.html">Iterative Methods</A> <B> <A NAME="tex2html1593" HREF="node1.html">Contents</A></B> <!--End of Navigation Panel--> </BODY> </HTML>