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This commit is contained in:
Salvatore Filippone
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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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>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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<TITLE>psb_precinit -- Initialize a preconditioner</TITLE>
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@@ -18,6 +18,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,370 +26,117 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BODY >
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HREF="node119.html">Iterative Methods</A>
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HREF="node121.html">psb_precbld Builds</A>
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HREF="node119.html">Preconditioner routines</A>
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HREF="node119.html">Preconditioner routines</A>
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<B> <A NAME="tex2html1743"
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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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><A NAME="SECTION000111000000000000000">
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psb_precinit -- Initialize a preconditioner</A>
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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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-->
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<IMG
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WIDTH="204" HEIGHT="44" BORDER="0"
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SRC="img156.png"
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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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<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\|}{\|b\|_2} < eps
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\end{displaymath}
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-->
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<IMG
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WIDTH="121" HEIGHT="44" BORDER="0"
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SRC="img157.png"
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ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < 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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according to the value passed through the istop argument (see
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later). In the above formulae, <IMG
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WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img158.png"
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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"
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SRC="img159.png"
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ALT="$r_i=b-Ax_i$"> the corresponding residual at the <IMG
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WIDTH="9" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img4.png"
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ALT="$i$">-th iteration.
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<P>
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<BR>
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<IMG
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WIDTH="482" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
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SRC="img160.png"
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ALT="\begin{lstlisting}
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call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
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& itmax,iter,err,itrace,irst,istop,cond)
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\end{lstlisting}">
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<BR>
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<PRE>
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call psb_precinit(prec, ptype, 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>Synchronous.
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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>method</STRONG></DT>
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<DD>a string that defines the iterative method to be
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used. Supported values are:
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<DL>
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<DT><STRONG>CG:</STRONG></DT>
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<DD>the Conjugate Gradient method;
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</DD>
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<DT><STRONG>CGS:</STRONG></DT>
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<DD>the Conjugate Gradient Stabilized method;
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<P>
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</DD>
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<DT><STRONG>BICG:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient method;
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</DD>
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<DT><STRONG>BICGSTAB:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient Stabilized method;
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</DD>
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<DT><STRONG>BICGSTABL:</STRONG></DT>
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<DD>the Bi-Conjugate Gradient Stabilized method with restarting;
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</DD>
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<DT><STRONG>RGMRES:</STRONG></DT>
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<DD>the Generalized Minimal Residual method with restarting.
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</DD>
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</DL>
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</DD>
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<DT><STRONG>a</STRONG></DT>
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<DD>the local portion of global sparse matrix
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<IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$">.
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<BR>
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Scope: <B>local</B>
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<DT><STRONG>ptype</STRONG></DT>
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<DD>the type of preconditioner.
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Scope: <B>global</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
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Specified as: a character string, see usage notes.
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</DD>
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<DT><STRONG><B>On Exit</B></STRONG></DT>
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<DD><P>
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</DD>
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<DT><STRONG>prec</STRONG></DT>
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<DD>The data structure containing the preconditioner.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a structured data of type precdata<TT>psb_prec_type</TT>.
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</DD>
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<DT><STRONG>b</STRONG></DT>
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<DD>The RHS vector.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
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</DD>
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<DT><STRONG>x</STRONG></DT>
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<DD>The initial guess.
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<BR>
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Scope: <B>local</B>
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<DD>Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>inout</B>.
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<BR>
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Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
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</DD>
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<DT><STRONG>eps</STRONG></DT>
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<DD>The stopping tolerance.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a real number.
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</DD>
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<DT><STRONG>desc_a</STRONG></DT>
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<DD>contains data structures for communications.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
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</DD>
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<DT><STRONG>itmax</STRONG></DT>
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<DD>The maximum number of iterations to perform.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Intent: <B>in</B>.
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<BR>
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Default: <IMG
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WIDTH="100" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img161.png"
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ALT="$itmax = 1000$">.
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<BR>
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Specified as: an integer variable <IMG
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WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img162.png"
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ALT="$itmax \ge 1$">.
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</DD>
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<DT><STRONG>itrace</STRONG></DT>
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<DD>If <IMG
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WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img112.png"
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ALT="$>0$"> print out an informational message about
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convergence every <IMG
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WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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SRC="img163.png"
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ALT="$itrace$"> iterations.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>
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<BR>
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Intent: <B>in</B>.
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<BR></DD>
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<DT><STRONG>irst</STRONG></DT>
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<DD>An integer specifying the restart parameter.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>.
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<BR>
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Intent: <B>in</B>.
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||||
<BR>
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Values: <IMG
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WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img164.png"
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ALT="$irst>0$">. This is employed for the BiCGSTABL or RGMRES
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methods, otherwise it is ignored.
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<P>
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</DD>
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<DT><STRONG>istop</STRONG></DT>
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<DD>An integer specifying the stopping criterion.
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<BR>
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Scope: <B>global</B>
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<BR>
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Type: <B>optional</B>.
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<BR>
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Intent: <B>in</B>.
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<BR>
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Values: 1: use the normwise backward error, 2: use the scaled 2-norm
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of the residual. Default: 2.
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</DD>
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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>x</STRONG></DT>
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<DD>The computed solution.
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<BR>
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Scope: <B>local</B>
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<BR>
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Type: <B>required</B>
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<BR>
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Intent: <B>inout</B>.
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<BR>
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Specified as: a rank one array or an object of type vdata<TT>psb_T_vect_type</TT>.
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</DD>
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<DT><STRONG>iter</STRONG></DT>
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<DD>The number of iterations performed.
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<BR>
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Scope: <B>global</B>
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<BR>
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||||
Type: <B>optional</B>
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<BR>
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Intent: <B>out</B>.
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<BR>
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Returned as: an integer variable.
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</DD>
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<DT><STRONG>err</STRONG></DT>
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<DD>The convergence estimate on exit.
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<BR>
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Scope: <B>global</B>
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||||
<BR>
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||||
Type: <B>optional</B>
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||||
<BR>
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||||
Intent: <B>out</B>.
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<BR>
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Returned as: a real number.
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</DD>
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<DT><STRONG>cond</STRONG></DT>
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<DD>An estimate of the condition number of matrix <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$">; only
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available with the <IMG
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WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img165.png"
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ALT="$CG$"> method.
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<BR>
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||||
Scope: <B>global</B>
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||||
<BR>
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||||
Type: <B>optional</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
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Returned as: a real number.
|
||||
Specified as: a preconditioner data structure precdata<TT>psb_prec_type</TT>.
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</DD>
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<DT><STRONG>info</STRONG></DT>
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<DD>Error code.
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||||
<DD>Scope: <B>global</B>
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
||||
Intent: <B>out</B>.
|
||||
<BR>
|
||||
An integer value; 0 means no error has been detected.
|
||||
Error code: if no error, 0 is returned.
|
||||
</DD>
|
||||
</DL>
|
||||
<FONT SIZE="+1"><B>Notes</B></FONT>
|
||||
Legal inputs to this subroutine are interpreted depending on the
|
||||
<IMG
|
||||
WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img155.png"
|
||||
ALT="$ptype$"> string as follows<A NAME="tex2html30"
|
||||
HREF="footnode.html#foot7458"><SUP>3</SUP></A>:
|
||||
<DL>
|
||||
<DT><STRONG>NONE</STRONG></DT>
|
||||
<DD>No preconditioning, i.e. the preconditioner is just a copy
|
||||
operator.
|
||||
</DD>
|
||||
<DT><STRONG>DIAG</STRONG></DT>
|
||||
<DD>Diagonal scaling; each entry of the input vector is
|
||||
multiplied by the reciprocal of the sum of the absolute values of
|
||||
the coefficients in the corresponding row of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">;
|
||||
</DD>
|
||||
<DT><STRONG>BJAC</STRONG></DT>
|
||||
<DD>Precondition by a factorization of the
|
||||
block-diagonal of matrix <IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="img1.png"
|
||||
ALT="$A$">, where block boundaries are determined
|
||||
by the data allocation boundaries for each process; requires no
|
||||
communication. Only the incomplete factorization <IMG
|
||||
WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="img156.png"
|
||||
ALT="$ILU(0)$"> is
|
||||
currently implemented.
|
||||
</DD>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
|
||||
<P>
|
||||
<HR>
|
||||
<!--Navigation Panel-->
|
||||
<A NAME="tex2html1731"
|
||||
HREF="node121.html">
|
||||
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
||||
<A NAME="tex2html1727"
|
||||
HREF="node119.html">
|
||||
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
||||
<A NAME="tex2html1723"
|
||||
HREF="node119.html">
|
||||
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
||||
<A NAME="tex2html1729"
|
||||
HREF="node1.html">
|
||||
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
||||
<BR>
|
||||
<B> Next:</B> <A NAME="tex2html1732"
|
||||
HREF="node121.html">Bibliography</A>
|
||||
<B> Up:</B> <A NAME="tex2html1728"
|
||||
HREF="node119.html">Iterative Methods</A>
|
||||
<B> Previous:</B> <A NAME="tex2html1724"
|
||||
HREF="node119.html">Iterative Methods</A>
|
||||
<B> <A NAME="tex2html1730"
|
||||
HREF="node1.html">Contents</A></B>
|
||||
<!--End of Navigation Panel-->
|
||||
<BR><HR>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
|
||||
Reference in New Issue
Block a user