You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
432 lines
10 KiB
HTML
432 lines
10 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
|
|
|
|
<!--Converted with LaTeX2HTML 2017.2 (Released Jan 23, 2017) -->
|
|
<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 v2017.2">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="userhtml.css">
|
|
|
|
<LINK REL="previous" HREF="node131.html">
|
|
<LINK REL="up" HREF="node131.html">
|
|
<LINK REL="next" HREF="node133.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
|
|
<DIV CLASS="navigation"><!--Navigation Panel-->
|
|
<A NAME="tex2html1904"
|
|
HREF="node133.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html1900"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html1896"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html1902"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html1905"
|
|
HREF="node133.html">Bibliography</A>
|
|
<B> Up:</B> <A NAME="tex2html1901"
|
|
HREF="node131.html">Iterative Methods</A>
|
|
<B> Previous:</B> <A NAME="tex2html1897"
|
|
HREF="node131.html">Iterative Methods</A>
|
|
<B> <A NAME="tex2html1903"
|
|
HREF="node1.html">Contents</A></B>
|
|
<BR>
|
|
<BR></DIV>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H2><A NAME="SECTION000121000000000000000"></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 can take the following values:
|
|
<DL>
|
|
<DT><STRONG>1</STRONG></DT>
|
|
<DD>normwise backward error in the infinity
|
|
norm; the iteration is stopped when
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="205" HEIGHT="44" BORDER="0"
|
|
SRC="img157.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>
|
|
</DD>
|
|
<DT><STRONG>2</STRONG></DT>
|
|
<DD>Relative residual in the 2-norm; the iteration is stopped
|
|
when
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
err = \frac{\|r_i\|}{\|b\|_2} < eps
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="121" HEIGHT="44" BORDER="0"
|
|
SRC="img158.png"
|
|
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
</DD>
|
|
<DT><STRONG>3</STRONG></DT>
|
|
<DD>Relative residual reduction in the 2-norm; the iteration is stopped
|
|
when
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER" CLASS="mathdisplay">
|
|
<!-- MATH
|
|
\begin{displaymath}
|
|
err = \frac{\|r_i\|}{\|r_0\|_2} < eps
|
|
\end{displaymath}
|
|
-->
|
|
|
|
<IMG
|
|
WIDTH="129" HEIGHT="44" BORDER="0"
|
|
SRC="img159.png"
|
|
ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\Vert _2} < eps \end{displaymath}">
|
|
</DIV>
|
|
<BR CLEAR="ALL">
|
|
<P></P>
|
|
</DD>
|
|
</DL>
|
|
The behaviour is controlled by the istop argument (see
|
|
later). In the above formulae, <SPAN CLASS="MATH"><IMG
|
|
WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img160.png"
|
|
ALT="$x_i$"></SPAN> is the tentative solution and
|
|
<SPAN CLASS="MATH"><IMG
|
|
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img161.png"
|
|
ALT="$r_i=b-Ax_i$"></SPAN> the corresponding residual at the <SPAN CLASS="MATH"><IMG
|
|
WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img4.png"
|
|
ALT="$i$"></SPAN>-th iteration.
|
|
|
|
<P>
|
|
<BR>
|
|
<IMG
|
|
WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img162.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>GCR:</STRONG></DT>
|
|
<DD>the Generalized Conjugate Residual method;
|
|
|
|
</DD>
|
|
<DT><STRONG>FCG:</STRONG></DT>
|
|
<DD>the Flexible Conjugate Gradient method<A NAME="tex2html32"
|
|
HREF="footnode.html#foot8093"><SUP><SPAN CLASS="arabic">5</SPAN></SUP></A>;
|
|
|
|
<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
|
|
<SPAN CLASS="MATH"><IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img1.png"
|
|
ALT="$A$"></SPAN>.
|
|
<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: <SPAN CLASS="MATH"><IMG
|
|
WIDTH="99" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img164.png"
|
|
ALT="$itmax = 1000$"></SPAN>.
|
|
<BR>
|
|
Specified as: an integer variable <SPAN CLASS="MATH"><IMG
|
|
WIDTH="76" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img165.png"
|
|
ALT="$itmax \ge 1$"></SPAN>.
|
|
</DD>
|
|
<DT><STRONG>itrace</STRONG></DT>
|
|
<DD>If <SPAN CLASS="MATH"><IMG
|
|
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img111.png"
|
|
ALT="$>0$"></SPAN> print out an informational message about
|
|
convergence every <SPAN CLASS="MATH"><IMG
|
|
WIDTH="45" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img166.png"
|
|
ALT="$itrace$"></SPAN> 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: <SPAN CLASS="MATH"><IMG
|
|
WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img167.png"
|
|
ALT="$irst>0$"></SPAN>. 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, 3: use the residual reduction in the 2-norm. 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 <SPAN CLASS="MATH"><IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img1.png"
|
|
ALT="$A$"></SPAN>; only
|
|
available with the <SPAN CLASS="MATH"><IMG
|
|
WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img168.png"
|
|
ALT="$CG$"></SPAN> method on real data.
|
|
<BR>
|
|
Scope: <B>global</B>
|
|
<BR>
|
|
Type: <B>optional</B>
|
|
<BR>
|
|
Intent: <B>out</B>.
|
|
<BR>
|
|
Returned as: a real number. A correct result will be greater than or
|
|
equal to one; if specified for non-real data, or an error occurred,
|
|
zero is returned.
|
|
</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>
|
|
|
|
<DIV CLASS="navigation"><HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html1904"
|
|
HREF="node133.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html1900"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html1896"
|
|
HREF="node131.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html1902"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html1905"
|
|
HREF="node133.html">Bibliography</A>
|
|
<B> Up:</B> <A NAME="tex2html1901"
|
|
HREF="node131.html">Iterative Methods</A>
|
|
<B> Previous:</B> <A NAME="tex2html1897"
|
|
HREF="node131.html">Iterative Methods</A>
|
|
<B> <A NAME="tex2html1903"
|
|
HREF="node1.html">Contents</A></B> </DIV>
|
|
<!--End of Navigation Panel-->
|
|
|
|
</BODY>
|
|
</HTML>
|