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Updated description of DOT and friends to account for optional GLOBAL
var.
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Salvatore Filippone
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@@ -3,8 +3,8 @@
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HREF="node133.html">psb_krylov Krylov</A>
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR></DIV>
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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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<H1><A NAME="SECTION000120000000000000000"></A>
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<A NAME="sec:methods"></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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Iterative Methods
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</H1>
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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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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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The stopping criterion can take the following values:
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<DL>
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<DT><STRONG>1</STRONG></DT>
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<DD>normwise backward error in the infinity
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norm; the iteration is stopped when
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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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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<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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<IMG
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WIDTH="205" 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 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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</DD>
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<DT><STRONG>2</STRONG></DT>
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<DD>Relative residual in the 2-norm; the iteration is stopped
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when
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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<!-- MATH
|
||||
\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="img158.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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</DD>
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<DT><STRONG>3</STRONG></DT>
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<DD>Relative residual reduction in the 2-norm; the iteration is stopped
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when
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<BR><P></P>
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<DIV ALIGN="CENTER" CLASS="mathdisplay">
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<!-- MATH
|
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\begin{displaymath}
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err = \frac{\|r_i\|}{\|r_0\|_2} < eps
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\end{displaymath}
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-->
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<IMG
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WIDTH="129" HEIGHT="44" BORDER="0"
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SRC="img159.png"
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ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\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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</DD>
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</DL>
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The behaviour is controlled by the istop argument (see
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later). In the above formulae, <SPAN CLASS="MATH"><IMG
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WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img160.png"
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ALT="$x_i$"></SPAN> is the tentative solution and
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<SPAN CLASS="MATH"><IMG
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WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
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SRC="img161.png"
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ALT="$r_i=b-Ax_i$"></SPAN> the corresponding residual at the <SPAN CLASS="MATH"><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="$i$"></SPAN>-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="img162.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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<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>
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<DT><STRONG><B>On Entry</B></STRONG></DT>
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<DD>
|
||||
</DD>
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<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>
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||||
<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#foot8086"><SUP><SPAN CLASS="arabic">5</SPAN></SUP></A>;
|
||||
|
||||
<P>
|
||||
</DD>
|
||||
<DT><STRONG>BICG:</STRONG></DT>
|
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<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>
|
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<BR>
|
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Intent: <B>in</B>.
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<BR>
|
||||
Specified as: a structured data of type spdata<TT>psb_Tspmat_type</TT>.
|
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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.
|
||||
<BR>
|
||||
Scope: <B>local</B>
|
||||
<BR>
|
||||
Type: <B>required</B>
|
||||
<BR>
|
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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>
|
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Intent: <B>in</B>.
|
||||
<BR>
|
||||
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.
|
||||
<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.
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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.
|
||||
<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
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WIDTH="99" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img164.png"
|
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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"
|
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HREF="node133.html">
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<A NAME="tex2html1900"
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HREF="node131.html">
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<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
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HREF="node131.html">
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<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
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<B> Next:</B> <A NAME="tex2html1905"
|
||||
HREF="node133.html">Bibliography</A>
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<B> Up:</B> <A NAME="tex2html1901"
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HREF="node131.html">Iterative Methods</A>
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<B> Previous:</B> <A NAME="tex2html1897"
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HREF="node131.html">Iterative Methods</A>
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<B> <A NAME="tex2html1903"
|
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HREF="node1.html">Contents</A></B> </DIV>
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<!--End of Navigation Panel-->
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<UL CLASS="ChildLinks">
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<LI><A NAME="tex2html1909"
|
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HREF="node133.html">psb_krylov -- Krylov Methods Driver
|
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Routine</A>
|
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</UL>
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<!--End of Table of Child-Links-->
|
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<BR><HR>
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</BODY>
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</HTML>
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Reference in New Issue
Block a user